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CURVA DE DOBLE MASA Y ANALISIS DE CONSISTENCIA/CURVA DOBLE MASA.xlsx CURVA DOBLE MASA Año estacion 1 estacion 2 estacion 1 estacion 2 PROMEDIO ACUMULADO 1953 629.5 629.50 0.00 314.75 314.75 1954 480.8 1110.30 0.00 555.15 869.90 1955 438.1 1548.40 0.00 774.20 1644.10 1956 424 1972.40 0.00 986.20 2630.30 1957 469.1 2441.50 0.00 1220.75 3851.05 1958 433.5 2875.00 0.00 1437.50 5288.55 1959 610.5 3485.50 0.00 1742.75 7031.30 1960 735 4220.50 0.00 2110.25 9141.55 1961 456.5 4677.00 0.00 2338.50 11480.05 1962 993.3 5670.30 0.00 2835.15 14315.20 1963 529 6199.30 0.00 3099.65 17414.85 1964 424.8 6624.10 0.00 3312.05 20726.90 1965 715.1 7339.20 0.00 3669.60 24396.50 1966 512.4 7851.60 0.00 3925.80 28322.30 1967 708.2 8559.80 0.00 4279.90 32602.20 1968 286.7 8846.50 0.00 4423.25 37025.45 1969 541.3 9387.80 0.00 4693.90 41719.35 1970 453.2 9841.00 0.00 4920.50 46639.85 1971 416 10257.00 0.00 5128.50 51768.35 1972 555.6 10812.60 0.00 5406.30 57174.65 1973 545.7 11358.30 0.00 5679.15 62853.80 1974 337.6 11695.90 0.00 5847.95 68701.75 1975 479.6 12175.50 0.00 6087.75 74789.50 1976 459.7 12635.20 0.00 6317.60 81107.10 1977 510.5 13145.70 0.00 6572.85 87679.95 1978 496.8 13642.50 0.00 6821.25 94501.20 1979 497.3 14139.80 0.00 7069.90 101571.10 1980 653 14792.80 0.00 7396.40 108967.50 1981 460.1 15252.90 0.00 7626.45 116593.95 1982 480.9 640.90 15733.80 640.90 8187.35 124781.30 1983 401.8 546.40 16135.60 1187.30 8661.45 133442.75 1984 455.3 812.44 16590.90 1999.74 9295.32 142738.07 1985 432 372.82 17022.90 2372.56 9697.73 152435.80 1986 554.5 617.00 17577.40 2989.56 10283.48 162719.28 1987 450.3 757.66 18027.70 3747.22 10887.46 173606.74 1988 726.4 607.30 18754.10 4354.52 11554.31 185161.05 1989 605.3 911.44 19359.40 5265.96 12312.68 197473.73 1990 577.5 472.70 19936.90 5738.65 12837.78 210311.51 1991 496.58 6235.24 6235.24 216546.75 1992 586.41 6821.65 6821.65 223368.39 1993 1126.80 7948.45 7948.45 231316.84 1994 544.17 8492.61 8492.61 239809.45 1995 561.30 9053.91 9053.91 248863.37 1996 525.50 9579.41 9579.41 258442.78 1997 220.00 9799.41 9799.41 268242.19 1998 670.05 10469.46 10469.46 278711.66 1999 657.60 11127.06 11127.06 289838.72 CURVA DOBLE MASA estacion 1 314.75000000000006 869.90000000000009 1644.1000000000001 2630.3 3851.05 5288.55 7031.3 9141.5499999999993 11480.05 14315.199999999999 17414.849999999999 20726.899999999998 24396.5 28322.3 32602.2 37025.450000000004 41719.350000000006 46639.850000000006 51768.350000000006 57174.650000000009 62853.80000000001 68701.750000000015 74789.500000000015 81107.10000000002 87679.950000000026 94501.200000000026 101571.10000000003 108967.50000000003 116593.95000000003 124781.30000000003 133442.75000000003 142738.0691176471 152435.79941478133 162719.2811833937 173606.74278362276 185161.05312282511 197473.73213842759 210311.50925946163 216546.74681883739 223368.39193235559 231316.83704587378 239809.45152213817 248863.36599840256 258442.78047466694 268242.19495093136 278711.65942719573 289838.72390346014 629.50000000000011 1110.3000000000002 1548.4 1972.4 2441.5 2875 3485.5 4220.5 4677 5670.3 6199.3 6624.1 7339.2000000000007 7851.6 8559.8000000000011 8846.5000000000018 9387.8000000000011 9841.0000000000018 10257.000000000002 10812.600000000002 11358.300000000003 11695.900000000003 12175.500000000004 12635.200000000004 13145.700000000004 13642.500000000004 14139.800000000003 14792.800000000003 15252.900000000003 15733.800000000003 16135.600000000002 16590.900000000001 17022.900000000001 17577.400000000001 18027.7 18754.100000000002 19359.400000000001 19936.900000000001 estacion 2 314.75000000000006 869.90000000000009 1644.1000000000001 2630.3 3851.05 5288.55 7031.3 9141.5499999999993 11480.05 14315.199999999999 17414.849999999999 20726.899999999998 24396.5 28322.3 32602.2 37025.450000000004 41719.350000000006 46639.850000000006 51768.350000000006 57174.650000000009 62853.80000000001 68701.750000000015 74789.500000000015 81107.10000000002 87679.950000000026 94501.200000000026 101571.10000000003 108967.50000000003 116593.95000000003 124781.30000000003 133442.75000000003 142738.0691176471 152435.79941478133 162719.2811833937 173606.74278362276 185161.05312282511 197473.73213842759 210311.50925946163 216546.74681883739 223368.39193235559 231316.83704587378 239809.45152213817 248863.36599840256 258442.78047466694 268242.19495093136 278711.65942719573 289838.72390346014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 640.90000000000009 1187.3000000000002 1999.7382352941177 2372.5605942684765 2989.5635372247275 3747.2232004580965 4354.5206784046823 5265.9580312049329 5738.6542420680653 6235.2375593757579 6821.6451135181851 7948.4451135181853 8492.614476264398 9053.9144762643973 9579.4144762643973 9799.4144762643973 10469.464476264397 11127.064476264397 CURVA DE DOBLE MASA Y ANALISIS DE CONSISTENCIA/estacion 1 analisis de consistencia.xlsx DATOS ESTACION 1 ESTACION 2 AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC a) Realice sus gráficos visual y doble masa 1953 46.7 122.1 146.4 46.3 6.7 0.1 0.2 0.2 23.4 82 111.2 44.2 1982 51.5 107.8 126.0 87.8 7.3 0.0 0.0 0.0 0.0 92.7 95.7 72.1 b) Hacer el análisis de consistencia entre las 2 estaciones 1954 84.6 64.4 120.3 35.2 13.5 0 0.3 0.1 1 22.8 40.7 97.9 1983 87.3 25.4 140.5 75.7 9.7 0.0 0.0 0.0 39.4 4.8 48.5 115.1 c) Hacer un análisis de tendencias en una de las 2 estaciones: considere sólo el análisis de 2 meses cualquiera 1955 48.5 67.8 117.9 s/d 6.7 0 0.1 0 1.3 33.6 47.7 114.5 1984 107.5 262.5 208.2 16.3 12.4 18.6 0.0 0.8 10.6 90.2 53.0 32.4 d) Haga la completación de datos tomando 2 meses como ejemplo, donde faltan datos 1956 28.5 65.7 152.6 79.1 26.7 0 0.3 0 2.5 47.9 8.6 12.1 1985 23.4 67.3 65.9 24.2 39.4 5.7 0.0 0.0 13.9 51.5 75.4 6.1 1957 54.7 58.2 118.7 33.2 32.2 0 0.5 0 12.5 28.3 28.5 102.3 1986 90.5 103.0 112.1 73.8 48.3 0.0 0.0 0.0 0.0 49.7 75.4 64.2 1958 38.6 93.1 162 96.9 4.5 0 0.7 0.1 0 9.6 9.3 18.7 1987 248.3 85.6 114.8 73.8 63.6 0.0 0.0 0.0 23.0 4.2 75.4 69.0 1959 44.8 96.9 224.2 48.8 56.6 0 0.1 10.1 0.2 25.1 37.8 65.9 1988 84.1 85.6 68.5 115.1 72.7 0.0 0.0 0.0 12.1 24.8 75.4 69.0 1960 71.8 196.5 165.3 68 1.9 0 0.1 0 21.5 121.5 58.1 30.3 1989 135.6 85.6 244.1 73.8 174.4 0.0 0.0 13.3 0.0 40.0 75.7 69.0 1961 46.8 54.4 110.4 s/d 6.9 0 0 1.9 0.5 44.4 73.1 118.1 1990 24.2 85.6 92.1 58.2 0.0 0.0 0.0 0.0 0.0 86.0 112.1 14.5 1962 36.3 146.8 155.1 62.5 1.8 0 0.1 0 255.4 191.1 86.7 57.5 1991 64.4 60.1 88.0 52.8 39.5 0.0 0.0 0.0 0.0 49.7 75.4 66.7 1963 71.1 112.5 134.6 73.9 0.1 0.1 0 0 0 9.7 65.7 61.3 1992 84.1 85.6 114.8 154.4 48.3 5.7 0.5 0.0 7.9 73.3 9.5 2.4 1964 25 46.6 155.3 65.9 0 0 7 0 3.5 57.4 62.6 1.5 1993 27.3 68.5 101.8 79.8 87.9 0.0 0.0 0.0 37.8 180.6 237.6 305.5 1965 49 215.6 198.1 63.8 42 0 0 0 3.5 43.5 19.4 80.2 1994 84.1 85.6 114.8 73.8 48.3 5.7 8.5 0.0 21.1 3.6 32.2 66.6 1966 72.3 61.6 91.8 55 4.4 0 0 0 2.1 115.6 57.1 52.5 1995 138.2 42.5 88.5 64.8 3.0 0.0 0.0 0.0 0.0 67.9 74.6 81.8 1967 98.8 196.3 158.6 33.9 12.7 0 10 14.7 31.7 83 22.5 46 1996 141.8 124.3 95.2 54.5 5.5 0.0 0.0 0.0 9.7 33.9 42.4 18.2 1968 34.1 50.2 111.5 15.8 22.8 0 0 0 0 10.6 32 9.7 1997 11.5 6.1 80.0 43.6 0.0 0.0 0.0 0.0 0.0 6.1 33.9 38.8 1969 21.2 67.8 104.1 84 11.7 0 0 1.6 0 62.9 75.2 112.8 1998 54.0 106.4 129.7 135.2 101.8 0.0 0.0 0.0 9.7 14.6 47.3 71.5 1970 36.3 74.1 166.6 55.5 23.9 0 1.5 0 11.2 66.8 9.7 7.6 1999 55.8 53.3 81.2 70.3 106.7 66.7 0.0 0.0 4.9 21.8 118.2 78.8 1971 36.3 74 142.9 82.8 3.5 0 0 0.4 0 19.2 41.5 15.4 1972 152.4 69.7 129.4 40.6 9.9 0 0.2 0.1 3.8 45.5 46.1 57.9 1973 58.6 57.5 103.7 55.2 11.1 0 0.2 0 1.3 36.6 93.5 128 1974 18.9 85.5 109 57.5 s/d 0 0.2 0.1 3 45.8 15.5 2.1 1975 72.5 85.7 113 51.5 13.8 0 0 0.2 2.3 35.7 13.1 91.8 1976 65.5 69.3 146.9 38.1 20 0 0 0 9.4 54.8 22.7 33 1977 83.7 104.2 143.6 35 20 0 0 0 1 30 45.8 47.2 1978 37.4 79.4 132.6 68.5 13.8 0 0 0 5 70.1 26.4 63.6 1979 41.9 89.5 138.5 75.7 5.1 0 0.3 0.6 2.3 43.3 43.5 56.6 1980 71.1 63.2 103.6 53.4 4.4 0.1 0 0 22.2 93.2 112.8 129 1981 43.5 113.8 133 39.7 11.7 0 0 0.1 0.5 21.1 39.1 57.6 1982 29.2 70.8 107.2 90.7 s/d 0 0.1 5.3 0.2 26 72.9 78.5 1983 37.2 70.2 110.2 75.6 8 0 0 0 2.4 48.5 13.4 36.3 1984 57.4 69 99.5 72.4 7.1 0 0.1 0 6.8 78.2 42.9 21.9 1985 24.3 61.6 133.9 55.4 6.8 0 0 0.1 3.6 72.1 19.6 54.6 1986 132.4 102.9 152.3 s/d 15.5 0 0 0.1 0.2 28 40.9 82.2 1987 48.9 91.2 120.5 59.1 3.8 0 0 0 5.7 68.2 37.8 15.1 1988 65.6 129.5 191.2 36 26.3 0 0.4 0 1.6 60.9 86.8 128.1 1989 64.6 180.8 227.7 s/d 21.6 0 0 0 4.5 52.9 26 27.2 1990 69.1 96.4 106 49.3 s/d 0 0 0 1.6 38.8 99.9 116.4 &"-,Negrita"Marcia Katherin Rojas Cabrejos E1ene Año Enero Salto 1953 46.7 1954 84.6 37.9 1955 48.5 36.1 1956 28.5 20 1957 54.7 26.2 1958 38.6 16.1 1959 44.8 6.2 1960 71.8 27 1961 46.8 25 1962 36.3 10.5 1963 71.1 34.8 1964 25 46.1 1965 49 24 1966 72.3 23.3 1967 98.8 26.5 1968 34.1 64.7 1969 21.2 12.9 1 2 1970 36.3 15.1 PERIODO 1953-1972 1973-1990 1971 36.3 0 n datos 20 18 1972 152.4 116.1 Promedio 54.89 56.7666666667 1973 58.6 93.8 S Des. Estandar 30.7279214705 26.2734936883 conprobacion de la varianza 1974 18.9 39.7 S2 Varianza 944.2051578947 690.2964705882 944.2051578947 690.2964705882 1975 72.5 53.6 1976 65.5 7 Sp = 28.7106919689 1977 83.7 18.2 1978 37.4 46.3 Sd = 9.3279070039 1979 41.9 4.5 1980 71.1 29.2 Tc = 0.201188398 1981 43.5 27.6 1982 29.2 14.3 Tt = 2.028094001 1983 37.2 8 1984 57.4 20.2 1985 24.3 33.1 1986 132.4 108.1 1987 48.9 83.5 FC = 1.3678255621 1988 65.6 16.7 1989 64.6 1 Ft = 2.2428907566 1990 69.1 4.5 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 54.89 56.7666666667 Varianza 944.2051578947 690.2964705882 Observaciones 20 18 Varianza agrupada 824.3038333333 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -0.201188398 P(T<=t) una cola 0.4208418548 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.8416837097 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 54.89 56.7666666667 Varianza 944.2051578947 690.2964705882 Observaciones 20 18 Grados de libertad 19 17 F 1.3678255621 P(F<=f) una cola 0.2603467185 Valor crítico para F (una cola) 2.2428907566 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 e1feb Año Febrero Salto 1953 122.1 1954 64.4 57.7 1955 67.8 3.4 1956 65.7 2.1 1957 58.2 7.5 1958 93.1 34.9 1959 96.9 3.8 1960 196.5 99.6 1961 54.4 142.1 1962 146.8 92.4 1963 112.5 34.3 1964 46.6 65.9 1965 215.6 169 1966 61.6 154 1967 196.3 134.7 1968 50.2 146.1 1969 67.8 17.6 1 2 1970 74.1 6.3 PERIODO 1953-1968 1969-1990 1971 74 0.1 n datos 16 22 1972 69.7 4.3 Promedio 103.04375 86.6409090909 1973 57.5 12.2 S Des. Estandar 57.0418789867 27.8686145211 conprobacion de la varianza 1974 85.5 28 S2 Varianza 3253.7759583333 776.6596753247 3253.7759583333 776.6596753247 1975 85.7 0.2 1976 69.3 16.4 Sp = 42.5298890183 1977 104.2 34.9 1978 79.4 24.8 Sd = 13.9738062058 1979 89.5 10.1 1980 63.2 26.3 Tc = 1.1738277079 1981 113.8 50.6 1982 70.8 43 Tt = 2.028094001 1983 70.2 0.6 1984 69 1.2 1985 61.6 7.4 1986 102.9 41.3 1987 91.2 11.7 FC = 4.1894488174 1988 129.5 38.3 1989 180.8 51.3 Ft = 0.4596286185 1990 96.4 84.4 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 86.6409090909 103.04375 Varianza 776.6596753247 3253.7759583333 Observaciones 22 16 Varianza agrupada 1808.7914599116 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -1.1738277079 P(T<=t) una cola 0.1240857208 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.2481714416 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 86.6409090909 103.04375 Varianza 776.6596753247 3253.7759583333 Observaciones 22 16 Grados de libertad 21 15 F 0.2386948841 P(F<=f) una cola 0.0014550048 Valor crítico para F (una cola) 0.4596286185 Febrero Febrero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 122.1 64.400000000000006 67.8 65.7 58.2 93.1 96.9 196.5 54.4 146.80000000000001 112.5 46.6 215.6 61.6 196.3 50.2 67.8 74.099999999999994 74 69.7 57.5 85.5 85.7 69.3 104.2 79.400000000000006 89.5 63.2 113.8 70.8 70.2 69 61.6 102.9 91.2 129.5 180.8 96.4 e1mar Año Marzo Salto 1953 146.4 1954 120.3 26.1 1955 117.9 2.4 1956 152.6 34.7 1957 118.7 33.9 1958 162 43.3 1959 224.2 62.2 1960 165.3 58.9 1961 110.4 54.9 1962 155.1 44.7 1963 134.6 20.5 1964 155.3 20.7 1965 198.1 42.8 1966 91.8 106.3 1967 158.6 66.8 1968 111.5 47.1 1969 104.1 7.4 1 2 1970 166.6 62.5 PERIODO 1953-1966 1967-1990 1971 142.9 23.7 n datos 14 24 1972 129.4 13.5 Promedio 146.6214285714 132.7291666667 1973 103.7 25.7 S Des. Estandar 35.2966587778 31.0311411491 conprobacion de la varianza 1974 109 5.3 S2 Varianza 1245.8541208791 962.9317210145 1245.8541208791 962.9317210145 1975 113 4 1976 146.9 33.9 Sp = 32.6358413893 1977 143.6 3.3 1978 132.6 11 Sd = 10.9753144875 1979 138.5 5.9 1980 103.6 34.9 Tc = 1.2657734701 1981 133 29.4 1982 107.2 25.8 Tt = 2.028094001 1983 110.2 3 1984 99.5 10.7 1985 133.9 34.4 1986 152.3 18.4 1987 120.5 31.8 FC = 1.293813563 1988 191.2 70.7 1989 227.7 36.5 Ft = 0.4597363529 1990 106 121.7 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 132.7291666667 146.6214285714 Varianza 962.9317210145 1245.8541208791 Observaciones 24 14 Varianza agrupada 1065.0981431878 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -1.2657734701 P(T<=t) una cola 0.1068624082 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.2137248163 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 132.7291666667 146.6214285714 Varianza 962.9317210145 1245.8541208791 Observaciones 24 14 Grados de libertad 23 13 F 0.7729088863 P(F<=f) una cola 0.2847547303 Valor crítico para F (una cola) 0.4597363529 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Marzo Marzo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 146.4 120.3 117.9 152.6 118.7 162 224.2 165.3 110.4 155.1 134.6 155.30000000000001 198.1 91.8 158.6 111.5 104.1 166.6 142.9 129.4 103.7 109 113 146.9 143.6 132.6 138.5 103.6 133 107.2 110.2 99.5 133.9 152.30000000000001 120.5 191.2 227.7 106 e1abr Año abril Salto 1953 46.3 1954 35.2 11.1 1955 35.2 1956 79.1 79.1 1957 33.2 45.9 1958 96.9 63.7 1959 48.8 48.1 1960 68 19.2 1961 68 1962 62.5 62.5 1963 73.9 11.4 1964 65.9 8 1965 63.8 2.1 1966 55 8.8 1967 33.9 21.1 1968 15.8 18.1 1969 84 68.2 1 2 1970 55.5 28.5 PERIODO 1953-1956 1957-1990 1971 82.8 27.3 n datos 3 31 1972 40.6 42.2 Promedio 53.5333333333 57.8612903226 1973 55.2 14.6 S Des. Estandar 22.8263736352 18.7626522187 conprobacion de la varianza 1974 57.5 2.3 S2 Varianza 521.0433333333 352.0371182796 521.0433333333 352.0371182796 1975 51.5 6 1976 38.1 13.4 Sp = 19.0420588887 1977 35 3.1 1978 68.5 33.5 Sd = 11.513619905 1979 75.7 7.2 1980 53.4 22.3 Tc = 0.3758988941 1981 39.7 13.7 1982 90.7 51 Tt = 2.0369333435 1983 75.6 15.1 1984 72.4 3.2 1985 55.4 17 1986 55.4 1987 59.1 59.1 FC = 1.4800806684 1988 36 23.1 1989 36 Ft = 0.3015836609 1990 49.3 49.3 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 57.8612903226 53.5333333333 Varianza 352.0371182796 521.0433333333 Observaciones 31 3 Varianza agrupada 362.6000067204 Diferencia hipotética de las medias 0 Grados de libertad 32 Estadístico t 0.3758988941 P(T<=t) una cola 0.3547363223 Valor crítico de t (una cola) 1.6938887484 P(T<=t) dos colas 0.7094726447 Valor crítico de t (dos colas) 2.0369333435 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 57.8612903226 53.5333333333 Varianza 352.0371182796 521.0433333333 Observaciones 31 3 Grados de libertad 30 2 F 0.6756388495 P(F<=f) una cola 0.2437692313 Valor crítico para F (una cola) 0.3015836609 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Abril abril 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.3 35.200000000000003 79.099999999999994 33.200000000000003 96.9 48.8 68 62.5 73.900000000000006 65.900000000000006 63.8 55 33.9 15.8 84 55.5 82.8 40.6 55.2 57.5 51.5 38.1 35 68.5 75.7 53.4 39.700000000000003 90.7 75.599999999999994 72.400000000000006 55.4 59.1 36 49.3 e1may Año Mayo Salto 1953 6.7 1954 13.5 6.8 1955 6.7 6.8 1956 26.7 20 1957 32.2 5.5 1958 4.5 27.7 1959 56.6 52.1 1960 1.9 54.7 1961 6.9 5 1962 1.8 5.1 1963 0.1 1.7 1964 0 0.1 1965 42 42 1966 4.4 37.6 1967 12.7 8.3 1968 22.8 10.1 1969 11.7 11.1 1 2 1970 23.9 12.2 PERIODO 1953-1960 1961-1990 1971 3.5 20.4 n datos 8 27 1972 9.9 6.4 Promedio 18.6 12.1740740741 1973 11.1 1.2 S Des. Estandar 18.8281703838 9.5917269077 conprobacion de la varianza 1974 11.1 S2 Varianza 354.5 92.0012250712 354.5 92.0012250712 1975 13.8 13.8 1976 20 6.2 Sp = 12.1524805447 1977 20 0 1978 13.8 6.2 Sd = 4.8918381659 1979 5.1 8.7 1980 4.4 0.7 Tc = 1.3136014946 1981 11.7 7.3 1982 11.7 Tt = 2.0345152974 1983 8 8 1984 7.1 0.9 1985 6.8 0.3 1986 15.5 8.7 1987 3.8 11.7 FC = 3.8532095603 1988 26.3 22.5 1989 21.6 4.7 Ft = 0.4187054696 1990 21.6 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 12.1740740741 18.6 Varianza 92.0012250712 354.5 Observaciones 27 8 Varianza agrupada 147.6827833895 Diferencia hipotética de las medias 0 Grados de libertad 33 Estadístico t -1.3136014946 P(T<=t) una cola 0.099020103 Valor crítico de t (una cola) 1.692360309 P(T<=t) dos colas 0.1980402059 Valor crítico de t (dos colas) 2.0345152974 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 12.1740740741 18.6 Varianza 92.0012250712 354.5 Observaciones 27 8 Grados de libertad 26 7 F 0.2595239071 P(F<=f) una cola 0.0052935537 Valor crítico para F (una cola) 0.4187054696 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Mayo Mayo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 6.7 13.5 6.7 26.7 32.200000000000003 4.5 56.6 1.9 6.9 1.8 0.1 0 42 4.4000000000000004 12.7 22.8 11.7 23.9 3.5 9.9 11.1 13.8 20 20 13.8 5.0999999999999996 4.4000000000000004 11.7 8 7.1 6.8 15.5 3.8 26.3 21.6 e1jun Año junio Salto 1953 0.1 1954 0 0.1 1955 0 0 1956 0 0 1957 0 0 1958 0 0 1959 0 0 1960 0 0 1961 0 0 1962 0 0 1963 0.1 0.1 1964 0 0.1 1965 0 0 1966 0 0 1967 0 0 1968 0 0 1969 0 0 1 2 1970 0 0 PERIODO 1953-1963 1964-1990 1971 0 0 n datos 11 18 1972 0 0 Promedio 0.0181818182 0.0037037037 1973 0 0 S Des. Estandar 0.0404519917 0.019245009 conprobacion de la varianza 1974 0 0 S2 Varianza 0.0016363636 0.0003703704 0.0016363636 0.0003703704 1975 0 0 1976 0 0 Sp = 0.0289699286 1977 0 0 1978 0 0 Sd = 0.0110869944 1979 0 0 1980 0.1 0.1 Tc = 1.3058646845 1981 0 0.1 1982 0 0 Tt = 2.028094001 1983 0 0 1984 0 0 1985 0 0 1986 0 0 1987 0 0 FC = 4.4181818182 1988 0 0 1989 0 0 Ft = 0.4505076621 1990 0 0 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 0.0037037037 0.0181818182 Varianza 0.0003703704 0.0016363636 Observaciones 27 11 Varianza agrupada 0.0007220352 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -1.5063269891 P(T<=t) una cola 0.070354247 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.1407084941 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 0.0037037037 0.0181818182 Varianza 0.0003703704 0.0016363636 Observaciones 27 11 Grados de libertad 26 10 F 0.2263374486 P(F<=f) una cola 0.0011008439 Valor crítico para F (una cola) 0.4505076621 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Junio Junio 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.1 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 e1jul Año julio Salto 1953 0.2 1954 0.3 0.1 1955 0.1 0.2 1956 0.3 0.2 1957 0.5 0.2 1958 0.7 0.2 1959 0.1 0.6 1960 0.1 0 1961 0 0.1 1962 0.1 0.1 1963 0 0.1 1964 7 7 1965 0 7 1966 0 0 1967 10 10 1968 0 10 1969 0 0 1 2 1970 1.5 1.5 PERIODO 1953-1965 1966-1990 1971 0 1.5 n datos 13 18 1972 0.2 0.2 Promedio 0.7230769231 0.52 1973 0.2 0 S Des. Estandar 1.8974341649 1.9987496091 conprobacion de la varianza 1974 0.2 0 S2 Varianza 3.6002564103 3.995 3.6002564103 3.995 1975 0 0.2 1976 0 0 Sp = 1.9574620877 1977 0 0 1978 0 0 Sd = 0.7124695002 1979 0.3 0.3 1980 0 0.3 Tc = 0.2850324442 1981 0 0 1982 0.1 0.1 Tt = 2.028094001 1983 0 0.1 1984 0.1 0.1 1985 0 0.1 1986 0 0 1987 0 0 FC = 1.1096431878 1988 0.4 0.4 1989 0 0.4 Ft = 2.5054815467 1990 0 0 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 0.52 0.7230769231 Varianza 3.995 3.6002564103 Observaciones 25 13 Varianza agrupada 3.8634188034 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -0.3021513661 P(T<=t) una cola 0.3821377403 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.7642754805 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 0.52 0.7230769231 Varianza 3.995 3.6002564103 Observaciones 25 13 Grados de libertad 24 12 F 1.1096431878 P(F<=f) una cola 0.4412376392 Valor crítico para F (una cola) 2.5054815467 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 julio julio 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.2 0.3 0.1 0.3 0.5 0.7 0.1 0.1 0 0.1 0 7 0 0 10 0 0 1.5 0 0.2 0.2 0.2 0 0 0 0 0.3 0 0 0.1 0 0.1 0 0 0 0.4 0 0 e1 ago Año agosto Salto 1953 0.2 1954 0.1 0.1 1955 0 0.1 1956 0 0 1957 0 0 1958 0.1 0.1 1959 10.1 10 1960 0 10.1 1961 1.9 1.9 1962 0 1.9 1963 0 0 1964 0 0 1965 0 0 1966 0 0 1967 14.7 14.7 1968 0 14.7 1969 1.6 1.6 1 2 1970 0 1.6 PERIODO 1953-1968 1969-1990 1971 0.4 0.4 n datos 16 22 1972 0.1 0.3 Promedio 1.69375 0.3909090909 1973 0 0.1 S Des. Estandar 4.2885069274 1.1525991708 conprobacion de la varianza 1974 0.1 0.1 S2 Varianza 18.3912916667 1.3284848485 18.3912916667 1.3284848485 1975 0.2 0.1 1976 0 0.2 Sp = 2.9048214557 1977 0 0 1978 0 0 Sd = 0.9544208325 1979 0.6 0.6 1980 0 0.6 Tc = 1.3650591696 1981 0.1 0.1 1982 5.3 5.2 Tt = 2.028094001 1983 0 5.3 1984 0 0 1985 0.1 0.1 1986 0.1 0 1987 0 0.1 FC = 13.8438098768 1988 0 0 1989 0 0 Ft = 0.4596286185 1990 0 0 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 0.3909090909 1.69375 Varianza 1.3284848485 18.3912916667 Observaciones 22 16 Varianza agrupada 8.4379876894 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -1.3650591696 P(T<=t) una cola 0.0903526299 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.1807052599 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 0.3909090909 1.69375 Varianza 1.3284848485 18.3912916667 Observaciones 22 16 Grados de libertad 21 15 F 0.0722344506 P(F<=f) una cola 0.0000001171 Valor crítico para F (una cola) 0.4596286185 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 agosto agosto 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.2 0.1 0 0 0 0.1 10.1 0 1.9 0 0 0 0 0 14.7 0 1.6 0 0.4 0.1 0 0.1 0.2 0 0 0 0.6 0 0.1 5.3 0 0 0.1 0.1 0 0 0 0 e1sep Año sep Salto 1953 23.4 1954 1 22.4 1955 1.3 0.3 1956 2.5 1.2 1957 12.5 10 1958 0 12.5 1959 0.2 0.2 1960 21.5 21.3 1961 0.5 21 1962 255.4 254.9 1963 0 255.4 1964 3.5 3.5 1965 3.5 0 1966 2.1 1.4 1967 31.7 29.6 1968 0 31.7 1969 0 0 1 2 1970 11.2 11.2 PERIODO 1953-1963 1964-1990 1971 0 11.2 n datos 11 27 1972 3.8 3.8 Promedio 28.9363636364 4.7925925926 1973 1.3 2.5 S Des. Estandar 75.6267184628 7.0850289574 conprobacion de la varianza 1974 3 1.7 S2 Varianza 5719.4005454545 50.1976353276 5719.4005454545 50.1976353276 1975 2.3 0.7 1976 9.4 7.1 Sp = 40.3109938041 1977 1 8.4 1978 5 4 Sd = 14.4190643088 1979 2.3 2.7 1980 22.2 19.9 Tc = 1.6744339665 1981 0.5 21.7 1982 0.2 0.3 Tt = 2.028094001 1983 2.4 2.2 1984 6.8 4.4 1985 3.6 3.2 1986 0.2 3.4 1987 5.7 5.5 FC = 113.937648818 1988 1.6 4.1 1989 4.5 2.9 Ft = 0.4505076621 1990 1.6 2.9 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 4.7925925926 28.9363636364 Varianza 50.1976353276 5719.4005454545 Observaciones 27 11 Varianza agrupada 1624.976221474 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -1.6744339665 P(T<=t) una cola 0.0513564488 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.1027128976 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 4.7925925926 28.9363636364 Varianza 50.1976353276 5719.4005454545 Observaciones 27 11 Grados de libertad 26 10 F 0.0087767302 P(F<=f) una cola 0 Valor crítico para F (una cola) 0.4505076621 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 sep sep 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 23.4 1 1.3 2.5 12.5 0 0.2 21.5 0.5 255.4 0 3.5 3.5 2.1 31.7 0 0 11.2 0 3.8 1.3 3 2.2999999999999998 9.4 1 5 2.2999999999999998 22.2 0.5 0.2 2.4 6.8 3.6 0.2 5.7 1.6 4.5 1.6 e1oct Año oct Salto 1953 82 1954 22.8 59.2 1955 33.6 10.8 1956 47.9 14.3 1957 28.3 19.6 1958 9.6 18.7 1959 25.1 15.5 1960 121.5 96.4 1961 44.4 77.1 1962 191.1 146.7 1963 9.7 181.4 1964 57.4 47.7 1965 43.5 13.9 1966 115.6 72.1 1967 83 32.6 1968 10.6 72.4 1969 62.9 52.3 1 2 1970 66.8 3.9 PERIODO 1953-1963 1964-1990 1971 19.2 47.6 n datos 11 27 1972 45.5 26.3 Promedio 56 52.1740740741 1973 36.6 8.9 S Des. Estandar 55.714612087 24.2078593816 conprobacion de la varianza 1974 45.8 9.2 S2 Varianza 3104.118 586.0204558405 3104.118 586.0204558405 1975 35.7 10.1 1976 54.8 19.1 Sp = 35.8537584625 1977 30 24.8 1978 70.1 40.1 Sd = 12.8247309281 1979 43.3 26.8 1980 93.2 49.9 Tc = 0.2983240699 1981 21.1 72.1 1982 26 4.9 Tt = 2.028094001 1983 48.5 22.5 1984 78.2 29.7 1985 72.1 6.1 1986 28 44.1 1987 68.2 40.2 FC = 5.2969447893 1988 60.9 7.3 1989 52.9 8 Ft = 0.4505076621 1990 38.8 14.1 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 52.1740740741 56 Varianza 586.0204558405 3104.118 Observaciones 27 11 Varianza agrupada 1285.4919958848 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -0.2983240699 P(T<=t) una cola 0.3835854901 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.7671709802 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 52.1740740741 56 Varianza 586.0204558405 3104.118 Observaciones 27 11 Grados de libertad 26 10 F 0.1887880731 P(F<=f) una cola 0.0002972105 Valor crítico para F (una cola) 0.4505076621 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 oct oct 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 82 22.8 33.6 47.9 28.3 9.6 25.1 121.5 44.4 191.1 9.6999999999999993 57.4 43.5 115.6 83 10.6 62.9 66.8 19.2 45.5 36.6 45.8 35.700000000000003 54.8 30 70.099999999999994 43.3 93.2 21.1 26 48.5 78.2 72.099999999999994 28 68.2 60.9 52.9 38.799999999999997 e1nov Año nov Salto 1953 111.2 1954 40.7 70.5 1955 47.7 7 1956 8.6 39.1 1957 28.5 19.9 1958 9.3 19.2 1959 37.8 28.5 1960 58.1 20.3 1961 73.1 15 1962 86.7 13.6 1963 65.7 21 1964 62.6 3.1 1965 19.4 43.2 1966 57.1 37.7 1967 22.5 34.6 1968 32 9.5 1969 75.2 43.2 1 2 1970 9.7 65.5 PERIODO 1953-1981 1982-1990 1971 41.5 31.8 n datos 29 9 1972 46.1 4.6 Promedio 46.4103448276 48.9111111111 1973 93.5 47.4 S Des. Estandar 29.3251153308 30.5772973153 conprobacion de la varianza 1974 15.5 78 S2 Varianza 859.9623891626 934.9711111111 859.9623891626 934.9711111111 1975 13.1 2.4 1976 22.7 9.6 Sp = 29.6079549115 1977 45.8 23.1 1978 26.4 19.4 Sd = 11.2974377072 1979 43.5 17.1 1980 112.8 69.3 Tc = 0.2213569438 1981 39.1 73.7 1982 72.9 33.8 Tt = 2.028094001 1983 13.4 59.5 1984 42.9 29.5 1985 19.6 23.3 1986 40.9 21.3 1987 37.8 3.1 FC = 1.0872232587 1988 86.8 49 1989 26 60.8 Ft = 0.4364403259 1990 99.9 73.9 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 46.4103448276 48.9111111111 Varianza 859.9623891626 934.9711111111 Observaciones 29 9 Varianza agrupada 876.63099404 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -0.2213569438 P(T<=t) una cola 0.4130326605 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.826065321 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 46.4103448276 48.9111111111 Varianza 859.9623891626 934.9711111111 Observaciones 29 9 Grados de libertad 28 8 F 0.9197742892 P(F<=f) una cola 0.400448383 Valor crítico para F (una cola) 0.4364403259 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 nov nov 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 111.2 40.700000000000003 47.7 8.6 28.5 9.3000000000000007 37.799999999999997 58.1 73.099999999999994 86.7 65.7 62.6 19.399999999999999 57.1 22.5 32 75.2 9.6999999999999993 41.5 46.1 93.5 15.5 13.1 22.7 45.8 26.4 43.5 112.8 39.1 72.900000000000006 13.4 42.9 19.600000000000001 40.9 37.799999999999997 86.8 26 99.9 e1dic Año dic Salto 1953 44.2 1954 97.9 53.7 1955 114.5 16.6 1956 12.1 102.4 1957 102.3 90.2 1958 18.7 83.6 1959 65.9 47.2 1960 30.3 35.6 1961 118.1 87.8 1962 57.5 60.6 1963 61.3 3.8 1964 1.5 59.8 1965 80.2 78.7 1966 52.5 27.7 1967 46 6.5 1968 9.7 36.3 1969 112.8 103.1 1 2 1970 7.6 105.2 PERIODO 1953-1974 1975-1990 1971 15.4 7.8 n datos 22 16 1972 57.9 42.5 Promedio 56.2045454545 64.94375 1973 128 70.1 S Des. Estandar 41.7164062424 36.5989793801 conprobacion de la varianza 1974 2.1 125.9 S2 Varianza 1740.2585497836 1339.4852916667 1740.2585497836 1339.4852916667 1975 91.8 89.7 1976 33 58.8 Sp = 39.6644638466 1977 47.2 14.2 1978 63.6 16.4 Sd = 13.0323295885 1979 56.6 7 1980 129 72.4 Tc = 0.6705788467 1981 57.6 71.4 1982 78.5 20.9 Tt = 2.028094001 1983 36.3 42.2 1984 21.9 14.4 1985 54.6 32.7 1986 82.2 27.6 1987 15.1 67.1 FC = 1.2991994467 1988 128.1 113 1989 27.2 100.9 Ft = 2.316317457 1990 116.4 89.2 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 56.2045454545 64.94375 Varianza 1740.2585497836 1339.4852916667 Observaciones 22 16 Varianza agrupada 1573.2696922349 Diferencia hipotética de las medias 0 Grados de libertad 36 Estadístico t -0.6705788467 P(T<=t) una cola 0.2533841983 Valor crítico de t (una cola) 1.6882977141 P(T<=t) dos colas 0.5067683966 Valor crítico de t (dos colas) 2.028094001 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 56.2045454545 64.94375 Varianza 1740.2585497836 1339.4852916667 Observaciones 22 16 Grados de libertad 21 15 F 1.2991994467 P(F<=f) una cola 0.3055551286 Valor crítico para F (una cola) 2.316317457 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 Enero Enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 dic dic 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 44.2 97.9 114.5 12.1 102.3 18.7 65.900000000000006 30.3 118.1 57.5 61.3 1.5 80.2 52.5 46 9.6999999999999993 112.8 7.6 15.4 57.9 128 2.1 91.8 33 47.2 63.6 56.6 129 57.6 78.5 36.299999999999997 21.9 54.6 82.2 15.1 128.1 27.2 116.4 analisis de datos Pp mensual corregido Año Enero Febrero Marzo Abril Mayo Junio Julio Agosto Setiembre Octubre Noviembre Diciembre pp total anual 1953 46.7 122.1 146.4 46.3 6.7 0.1 0.2 0.2 23.4 82 111.2 44.2 629.5 1954 84.6 64.4 120.3 35.2 13.5 0 0.3 0.1 1 22.8 40.7 97.9 480.8 1955 48.5 67.8 117.9 0 6.7 0 0.1 0 1.3 33.6 47.7 114.5 438.1 1956 28.5 65.7 152.6 79.1 26.7 0 0.3 0 2.5 47.9 8.6 12.1 424 1957 54.7 58.2 118.7 33.2 32.2 0 0.5 0 12.5 28.3 28.5 102.3 469.1 1958 38.6 93.1 162 96.9 4.5 0 0.7 0.1 0 9.6 9.3 18.7 433.5 1959 44.8 96.9 224.2 48.8 56.6 0 0.1 10.1 0.2 25.1 37.8 65.9 610.5 1960 71.8 196.5 165.3 68 1.9 0 0.1 0 21.5 121.5 58.1 30.3 735 1961 46.8 54.4 110.4 0 6.9 0 0 1.9 0.5 44.4 73.1 118.1 456.5 1962 36.3 146.8 155.1 62.5 1.8 0 0.1 0 255.4 191.1 86.7 57.5 993.3 1963 71.1 112.5 134.6 73.9 0.1 0.1 0 0 0 9.7 65.7 61.3 529 1964 25 46.6 155.3 65.9 0 0 7 0 3.5 57.4 62.6 1.5 424.8 1965 49 215.6 198.1 63.8 42 0 0 0 3.5 43.5 19.4 80.2 715.1 1966 72.3 61.6 91.8 55 4.4 0 0 0 2.1 115.6 57.1 52.5 512.4 1967 98.8 196.3 158.6 33.9 12.7 0 10 14.7 31.7 83 22.5 46 708.2 1968 34.1 50.2 111.5 15.8 22.8 0 0 0 0 10.6 32 9.7 286.7 1969 21.2 67.8 104.1 84 11.7 0 0 1.6 0 62.9 75.2 112.8 541.3 1970 36.3 74.1 166.6 55.5 23.9 0 1.5 0 11.2 66.8 9.7 7.6 453.2 1971 36.3 74 142.9 82.8 3.5 0 0 0.4 0 19.2 41.5 15.4 416 1972 152.4 69.7 129.4 40.6 9.9 0 0.2 0.1 3.8 45.5 46.1 57.9 555.6 1973 58.6 57.5 103.7 55.2 11.1 0 0.2 0 1.3 36.6 93.5 128 545.7 1974 18.9 85.5 109 57.5 0 0 0.2 0.1 3 45.8 15.5 2.1 337.6 1975 72.5 85.7 113 51.5 13.8 0 0 0.2 2.3 35.7 13.1 91.8 479.6 1976 65.5 69.3 146.9 38.1 20 0 0 0 9.4 54.8 22.7 33 459.7 1977 83.7 104.2 143.6 35 20 0 0 0 1 30 45.8 47.2 510.5 1978 37.4 79.4 132.6 68.5 13.8 0 0 0 5 70.1 26.4 63.6 496.8 1979 41.9 89.5 138.5 75.7 5.1 0 0.3 0.6 2.3 43.3 43.5 56.6 497.3 1980 71.1 63.2 103.6 53.4 4.4 0.1 0 0 22.2 93.2 112.8 129 653 1981 43.5 113.8 133 39.7 11.7 0 0 0.1 0.5 21.1 39.1 57.6 460.1 1982 29.2 70.8 107.2 90.7 0 0 0.1 5.3 0.2 26 72.9 78.5 480.9 1983 37.2 70.2 110.2 75.6 8 0 0 0 2.4 48.5 13.4 36.3 401.8 1984 57.4 69 99.5 72.4 7.1 0 0.1 0 6.8 78.2 42.9 21.9 455.3 1985 24.3 61.6 133.9 55.4 6.8 0 0 0.1 3.6 72.1 19.6 54.6 432 1986 132.4 102.9 152.3 0 15.5 0 0 0.1 0.2 28 40.9 82.2 554.5 1987 48.9 91.2 120.5 59.1 3.8 0 0 0 5.7 68.2 37.8 15.1 450.3 1988 65.6 129.5 191.2 36 26.3 0 0.4 0 1.6 60.9 86.8 128.1 726.4 1989 64.6 180.8 227.7 0 21.6 0 0 0 4.5 52.9 26 27.2 605.3 1990 69.1 96.4 106 49.3 0 0 0 0 1.6 38.8 99.9 116.4 577.5 ANALISIS DE TENDENCIAS ENE FEB MAR ABR MAY JUN JUL AGO SEP OCT NOV DIC r2 = 0.0149 2.00E-05 0.0072 0.001 0.026 0.0271 0.0237 0.0172 0.0291 0.001 0.0003 0.0017 N = 38 38 38 38 38 38 38 38 38 38 38 38 Tc = 0.738 0.027 0.511 0.190 0.980 1.001 0.935 0.794 1.039 0.190 0.104 0.248 P = 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975 Tt = 2.028 2.028 2.028 2.028 2.028 2.028 2.028 2.028 2.028 2.028 2.028 2.028 Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Tc<Tt Enero enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.7 84.6 48.5 28.5 54.7 38.6 44.8 71.8 46.8 36.299999999999997 71.099999999999994 25 49 72.3 98.8 34.1 21.2 36.299999999999997 36.299999999999997 152.4 58.6 18.899999999999999 72.5 65.5 83.7 37.4 41.9 71.099999999999994 43.5 29.2 37.200000000000003 57.4 24.3 132.4 48.9 65.599999999999994 64.599999999999994 69.099999999999994 oct Octubre 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 82 22.8 33.6 47.9 28.3 9.6 25.1 121.5 44.4 191.1 9.6999999999999993 57.4 43.5 115.6 83 10.6 62.9 66.8 19.2 45.5 36.6 45.8 35.700000000000003 54.8 30 70.099999999999994 43.3 93.2 21.1 26 48.5 78.2 72.099999999999994 28 68.2 60.9 52.9 38.799999999999997 nov Noviembre 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 111.2 40.700000000000003 47.7 8.6 28.5 9.3000000000000007 37.799999999999997 58.1 73.099999999999994 86.7 65.7 62.6 19.399999999999999 57.1 22.5 32 75.2 9.6999999999999993 41.5 46.1 93.5 15.5 13.1 22.7 45.8 26.4 43.5 112.8 39.1 72.900000000000006 13.4 42.9 19.600000000000001 40.9 37.799999999999997 86.8 26 99.9 dic Diciembre 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 44.2 97.9 114.5 12.1 102.3 18.7 65.900000000000006 30.3 118.1 57.5 61.3 1.5 80.2 52.5 46 9.6999999999999993 112.8 7.6 15.4 57.9 128 2.1 91.8 33 47.2 63.6 56.6 129 57.6 78.5 36.299999999999997 21.9 54.6 82.2 15.1 128.1 27.2 116.4 febrero enero 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 122.1 64.4000 00000000006 67.8 65.7 58.2 93.1 96.9 196.5 54.4 146.80000000000001 112.5 46.6 215.6 61.6 196.3 50.2 67.8 74.099999999999994 74 69.7 57.5 85.5 85.7 69.3 104.2 79.400000000000006 89.5 63.2 113.8 70.8 70.2 69 61.6 102.9 91.2 129.5 180.8 96.4 marzo Marzo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 146.4 120.3 117.9 152.6 118.7 162 224.2 165.3 110.4 155.1 134.6 155.30000000000001 198.1 91.8 158.6 111.5 104.1 166.6 142.9 129.4 103.7 109 113 146.9 143.6 132.6 138.5 103.6 133 107.2 110.2 99.5 133.9 152.30000000000001 120.5 191.2 227.7 106 abril Abril 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 46.3 35.200000000000003 0 79.099999999999994 33.200000000000003 96.9 48.8 68 0 62.5 73.900000000000006 65.900000000000006 63.8 55 33.9 15.8 84 55.5 82.8 40.6 55.2 57.5 51.5 38.1 35 68.5 75.7 53.4 39.700000000000003 90.7 75.599999999999994 72.400000000000006 55.4 0 59.1 36 0 49.3 mayo Mayo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 6.7 13.5 6.7 26.7 32.200000000000003 4.5 56.6 1.9 6.9 1.8 0.1 0 42 4.4000000000000004 12.7 22.8 11.7 23.9 3.5 9.9 11.1 0 13.8 20 20 13.8 5.0999999999999996 4.4000000000000004 11.7 0 8 7.1 6.8 15.5 3.8 26.3 21.6 0 junio Marzo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.1 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 0 0 0 0 julio Marzo 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.2 0.3 0.1 0.3 0.5 0.7 0.1 0.1 0 0.1 0 7 0 0 10 0 0 1.5 0 0.2 0.2 0.2 0 0 0 0 0.3 0 0 0.1 0 0.1 0 0 0 0.4 0 0 agosto Agosto 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 0.2 0.1 0 0 0 0.1 10.1 0 1.9 0 0 0 0 0 14.7 0 1.6 0 0.4 0.1 0 0.1 0.2 0 0 0 0.6 0 0.1 5.3 0 0 0.1 0.1 0 0 0 0 sep Setiembre 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 23.4 1 1.3 2.5 12.5 0 0.2 21.5 0.5 255.4 0 3.5 3.5 2.1 31.7 0 0 11.2 0 3.8 1.3 3 2.2999999999999998 9.4 1 5 2.2999999999999998 22.2 0.5 0.2 2.4 6.8 3.6 0.2 5.7 1.6 4.5 1.6 x x ( ) ( ) 12 1 2 12 1 22 2 1122 12 12 11 11 2 = desviacion estandar de las diferencia s de los promedios = desviacion estandar de ponderada Si || (95%) (est c d p d p d p ct xx T S SS nn nSnS S nn S S TTxx æö - = ç÷ ç÷ èø éù =+ êú ëû éù -+- êú +- êú ëû £= 12 adisticamente) En este caso, no se realiza proceso de c orreccion. Si || (95%) En este caso, que se presenta diferencia estadistica, se debe correguir la información ct TTxx CONSISTENCIADELADESVI ³¹ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 11 1 1 1 2 2 2 22 1 2 2 1 22 12 2 2 2 2 22 21 2 1 1 2 var : 1 1 1 1 ...1 ... n i n i ACIONESTANDAR Calculodelaianciasdeambosperiodos Sxxix n Sxxix n CalculodeFcalculadoFC Sx FcsiSxSx Sx Sx FcsiSxSx Sx GLNn GLDn = = =- - =- - => => =- =- å å ( ) ( ) ( ) ( ) 22 12 2 22 121 1 ...1 ...1 G.L.N. = grados de libertad del numerado r G.L.D. = grados de libertad del denomina dor Comparacion del Fc con el Ft . S siSxSx GLNn GLDnsiSxSx > =- =-> 12 12 i: Fc Ft (95%) .(x) = (x) (estadistica mente) . Si: Fc > Ft (95%) .(x) (x) (estadist icamente) Por lo que se debe corregir. de de SS SS TcTcalculado xpromedio ttTtablas FcFcalculado FtFtabla £® ®¹ = = = = = s 12121212221122121211112 = desviacion estandar de las diferencias de los promedios = desviacion estandar de ponderadaSi || (95%) (estcdpdpdpctxxTSSSnnnSnSSnnSSTTxx12adisticamente)En este caso, no se realiza proceso de correccion.Si || (95%) En este caso, que se presenta diferencia estadistica, se debe correguir la información ctTTxxCONSISTENCIADELADESVI1122111112222212212212222222212112 var :1111 ...1...niniACIONESTANDARCalculodelaianciasdeambosperiodosSxxixnSxxixnCalculodeFcalculadoFCSxFcsiSxSxSxSxFcsiSxSxSxGLNnGLDn22122221211 ...1...1 G.L.N. = grados de libertad del numeradorG.L.D. = grados de libertad del denominadorComparacion del Fc con el Ft. SsiSxSxGLNnGLDnsiSxSx1212i: Fc Ft (95%) .(x) = (x) (estadisticamente). Si: Fc > Ft (95%) .(x) (x) (estadisticamente)Por lo que se debe corregir. de de SSSSTcTcalculadoxpromediottTtablasFcFcalculadoFtFtablas ( ) 11 tcttxxestadisticamente <= 11 tcttxxestadisticamente CURVA DE DOBLE MASA Y ANALISIS DE CONSISTENCIA/estacion 2 analsiis de consitencia.xlsx DATOS ESTACION 1 ESTACION 2 AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC a) Realice sus gráficos visual y doble masa 1953 46.7 122.1 146.4 46.3 6.7 0.1 0.2 0.2 23.4 82 111.2 44.2 1982 51.5 107.8 126.0 87.8 7.3 0.0 0.0 0.0 0.0 92.7 95.7 72.1 b) Hacer el análisis de consistencia entre las 2 estaciones 1954 84.6 64.4 120.3 35.2 13.5 0 0.3 0.1 1 22.8 40.7 97.9 1983 87.3 25.4 140.5 75.7 9.7 0.0 0.0 0.0 39.4 4.8 48.5 115.1 c) Hacer un análisis de tendencias en una de las 2 estaciones: considere sólo el análisis de 2 meses cualquiera 1955 48.5 67.8 117.9 s/d 6.7 0 0.1 0 1.3 33.6 47.7 114.5 1984 107.5 262.5 208.2 16.3 12.4 18.6 0.0 0.8 10.6 90.2 53.0 32.4 d) Haga la completación de datos tomando 2 meses como ejemplo, donde faltan datos 1956 28.5 65.7 152.6 79.1 26.7 0 0.3 0 2.5 47.9 8.6 12.1 1985 23.4 67.3 65.9 24.2 39.4 5.7 0.0 0.0 13.9 51.5 75.4 6.1 1957 54.7 58.2 118.7 33.2 32.2 0 0.5 0 12.5 28.3 28.5 102.3 1986 90.5 103.0 112.1 73.8 48.3 0.0 0.0 0.0 0.0 49.7 75.4 64.2 1958 38.6 93.1 162 96.9 4.5 0 0.7 0.1 0 9.6 9.3 18.7 1987 248.3 85.6 114.8 73.8 63.6 0.0 0.0 0.0 23.0 4.2 75.4 69.0 1959 44.8 96.9 224.2 48.8 56.6 0 0.1 10.1 0.2 25.1 37.8 65.9 1988 84.1 85.6 68.5 115.1 72.7 0.0 0.0 0.0 12.1 24.8 75.4 69.0 1960 71.8 196.5 165.3 68 1.9 0 0.1 0 21.5 121.5 58.1 30.3 1989 135.6 85.6 244.1 73.8 174.4 0.0 0.0 13.3 0.0 40.0 75.7 69.0 1961 46.8 54.4 110.4 s/d 6.9 0 0 1.9 0.5 44.4 73.1 118.1 1990 24.2 85.6 92.1 58.2 0.0 0.0 0.0 0.0 0.0 86.0 112.1 14.5 1962 36.3 146.8 155.1 62.5 1.8 0 0.1 0 255.4 191.1 86.7 57.5 1991 64.4 60.1 88.0 52.8 39.5 0.0 0.0 0.0 0.0 49.7 75.4 66.7 1963 71.1 112.5 134.6 73.9 0.1 0.1 0 0 0 9.7 65.7 61.3 1992 84.1 85.6 114.8 154.4 48.3 5.7 0.5 0.0 7.9 73.3 9.5 2.4 1964 25 46.6 155.3 65.9 0 0 7 0 3.5 57.4 62.6 1.5 1993 27.3 68.5 101.8 79.8 87.9 0.0 0.0 0.0 37.8 180.6 237.6 305.5 1965 49 215.6 198.1 63.8 42 0 0 0 3.5 43.5 19.4 80.2 1994 84.1 85.6 114.8 73.8 48.3 5.7 8.5 0.0 21.1 3.6 32.2 66.6 1966 72.3 61.6 91.8 55 4.4 0 0 0 2.1 115.6 57.1 52.5 1995 138.2 42.5 88.5 64.8 3.0 0.0 0.0 0.0 0.0 67.9 74.6 81.8 1967 98.8 196.3 158.6 33.9 12.7 0 10 14.7 31.7 83 22.5 46 1996 141.8 124.3 95.2 54.5 5.5 0.0 0.0 0.0 9.7 33.9 42.4 18.2 1968 34.1 50.2 111.5 15.8 22.8 0 0 0 0 10.6 32 9.7 1997 11.5 6.1 80.0 43.6 0.0 0.0 0.0 0.0 0.0 6.1 33.9 38.8 1969 21.2 67.8 104.1 84 11.7 0 0 1.6 0 62.9 75.2 112.8 1998 54.0 106.4 129.7 135.2 101.8 0.0 0.0 0.0 9.7 14.6 47.3 71.5 1970 36.3 74.1 166.6 55.5 23.9 0 1.5 0 11.2 66.8 9.7 7.6 1999 55.8 53.3 81.2 70.3 106.7 66.7 0.0 0.0 4.9 21.8 118.2 78.8 1971 36.3 74 142.9 82.8 3.5 0 0 0.4 0 19.2 41.5 15.4 1972 152.4 69.7 129.4 40.6 9.9 0 0.2 0.1 3.8 45.5 46.1 57.9 1973 58.6 57.5 103.7 55.2 11.1 0 0.2 0 1.3 36.6 93.5 128 1974 18.9 85.5 109 57.5 s/d 0 0.2 0.1 3 45.8 15.5 2.1 1975 72.5 85.7 113 51.5 13.8 0 0 0.2 2.3 35.7 13.1 91.8 1976 65.5 69.3 146.9 38.1 20 0 0 0 9.4 54.8 22.7 33 1977 83.7 104.2 143.6 35 20 0 0 0 1 30 45.8 47.2 1978 37.4 79.4 132.6 68.5 13.8 0 0 0 5 70.1 26.4 63.6 1979 41.9 89.5 138.5 75.7 5.1 0 0.3 0.6 2.3 43.3 43.5 56.6 1980 71.1 63.2 103.6 53.4 4.4 0.1 0 0 22.2 93.2 112.8 129 1981 43.5 113.8 133 39.7 11.7 0 0 0.1 0.5 21.1 39.1 57.6 1982 29.2 70.8 107.2 90.7 s/d 0 0.1 5.3 0.2 26 72.9 78.5 1983 37.2 70.2 110.2 75.6 8 0 0 0 2.4 48.5 13.4 36.3 1984 57.4 69 99.5 72.4 7.1 0 0.1 0 6.8 78.2 42.9 21.9 1985 24.3 61.6 133.9 55.4 6.8 0 0 0.1 3.6 72.1 19.6 54.6 1986 132.4 102.9 152.3 s/d 15.5 0 0 0.1 0.2 28 40.9 82.2 1987 48.9 91.2 120.5 59.1 3.8 0 0 0 5.7 68.2 37.8 15.1 1988 65.6 129.5 191.2 36 26.3 0 0.4 0 1.6 60.9 86.8 128.1 1989 64.6 180.8 227.7 s/d 21.6 0 0 0 4.5 52.9 26 27.2 1990 69.1 96.4 106 49.3 s/d 0 0 0 1.6 38.8 99.9 116.4 &"-,Negrita"Marcia Katherin Rojas Cabrejos ene Año Enero Salto 1982 51.5 1983 87.3 35.8 1984 107.5 20.2 1985 23.4 84.1 1986 90.5 67.1 1987 248.3 157.8 1988 84.1 164.2157585576 1989 135.6 51.5157585576 1990 24.2 111.4 1991 64.4 40.2336216364 1992 84.1 19.650619806 1993 27.3 56.7842414424 1994 84.1 56.7842414424 1995 138.2 54.1157585576 1996 141.8 3.6 1997 11.5 130.28 1998 54.0 42.43 1 2 1999 55.8 1.81 PERIODO 1982-1988 1989-1999 n datos 7 11 Promedio 98.9 74.6 S Des. Estandar 71.6076638819 47.0137760596 conprobacion de la varianza S2 Varianza 5127.6575266252 2210.2951393834 5127.6575266252 2210.2951393834 Sp = 57.4830934675 Sd = 27.7927180556 Tc = 0.8747044658 Tt = 2.1199052992 FC = 2.3198972098 Ft = 0.3108317517 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 74.6301913201 98.9406059203 Varianza 2210.2951393834 5127.6575266252 Observaciones 11 7 Varianza agrupada 3304.306034599 Diferencia hipotética de las medias 0 Grados de libertad 16 Estadístico t -0.8747044658 P(T<=t) una cola 0.197337765 Valor crítico de t (una cola) 1.7458836763 P(T<=t) dos colas 0.3946755301 Valor crítico de t (dos colas) 2.1199052992 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 74.6301913201 98.9406059203 Varianza 2210.2951393834 5127.6575266252 Observaciones 11 7 Grados de libertad 10 6 F 0.4310535811 P(F<=f) una cola 0.1148085779 Valor crítico para F (una cola) 0.3108317517 Enero Enero 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 51.5 87.3 107.5 23.4 90.5 248.3 84.084241442428336 135.6 24.2 64.433621636425215 84.084241442428336 27.3 84.084241442428336 138.19999999999999 141.80000000000001 11.52 53.95 55.76 feb Año FEB Salto 1982 107.8 1983 25.4 82.4 1984 262.5 237.1 1985 67.3 195.2 1986 103.0 35.7 1987 85.6 17.4037891369 1988 85.6 0 1989 85.6 0 1990 85.6 0 1991 60.1 25.5216805055 1992 85.6 25.5216805055 1993 68.5 17.0962108631 1994 85.6 17.0962108631 1995 42.5 43.0962108631 1996 124.3 81.8 1997 6.1 118.24 1998 106.4 100.32 1 2 1999 53.3 53.04 PERIODO 1982-1995 1996-1999 n datos 14 4 Promedio 89.3 72.5 S Des. Estandar 54.5292383248 53.5800709219 conprobacion de la varianza S2 Varianza 2973.4378322845 2870.824 2973.4378322845 2870.824 Sp = 54.3525320361 Sd = 30.8149891916 Tc = 0.5455874414 Tt = 2.1199052992 FC = 1.0357436862 Ft = 8.7286812466 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 89.3322711097 72.52 Varianza 2973.4378322845 2870.824 Observaciones 14 4 Varianza agrupada 2954.1977387312 Diferencia hipotética de las medias 0 Grados de libertad 16 Estadístico t 0.5455874414 P(T<=t) una cola 0.296437588 Valor crítico de t (una cola) 1.7458836763 P(T<=t) dos colas 0.5928751759 Valor crítico de t (dos colas) 2.1199052992 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 89.3322711097 72.52 Varianza 2973.4378322845 2870.824 Observaciones 14 4 Grados de libertad 13 3 F 1.0357436862 P(F<=f) una cola 0.5615899378 Valor crítico para F (una cola) 8.7286812466 Febrero FEB 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 107.8 25.4 262.5 67.3 103 85.596210863132185 85.596210863132185 85.596210863132185 85.596210863132185 60.074530357586383 85.596210863132185 68.5 85.596210863132185 42.5 124.3 6.06 106.38 53.34 MAR 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 126 140.5 208.2 65.900000000000006 112.1 114.78461812542623 68.5 244.1 92.1 87.959271881393278 114.78461812542623 101.8 114.78461812542623 88.5 95.2 80 129.69999999999999 81.209999999999994 mar Año MAR Salto 1982 126.0 1983 140.5 14.5 1984 208.2 67.7 1985 65.9 142.3 1986 112.1 46.2 1987 114.8 2.6846181254 1988 68.5 46.2846181254 1989 244.1 175.6 1990 92.1 152 1991 88.0 4.1407281186 1992 114.8 26.825346244 1993 101.8 12.9846181254 1994 114.8 12.9846181254 1995 88.5 26.2846181254 1996 95.2 6.7 1997 80.0 15.2 1998 129.7 49.7 1 2 1999 81.2 48.49 PERIODO 1982-1988 1989-1999 n datos 7 11 Promedio 119.4 111.8 S Des. Estandar 48.1349784127 46.5439726397 conprobacion de la varianza S2 Varianza 2316.9761467877 2166.3413890866 2316.9761467877 2166.3413890866 Sp = 47.1468919784 Sd = 22.7952289432 Tc = 0.3332101016 Tt = 2.1199052992 FC = 1.0695341734 Ft = 0.3108317517 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 74.6301913201 98.9406059203 Varianza 2210.2951393834 5127.6575266252 Observaciones 11 7 Varianza agrupada 3304.306034599 Diferencia hipotética de las medias 0 Grados de libertad 16 Estadístico t -0.8747044658 P(T<=t) una cola 0.197337765 Valor crítico de t (una cola) 1.7458836763 P(T<=t) dos colas 0.3946755301 Valor crítico de t (dos colas) 2.1199052992 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 74.6301913201 98.9406059203 Varianza 2210.2951393834 5127.6575266252 Observaciones 11 7 Grados de libertad 10 6 F 0.4310535811 P(F<=f) una cola 0.1148085779 Valor crítico para F (una cola) 0.3108317517 Enero Enero 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 51.5 87.3 107.5 23.4 90.5 248.3 84.084241442428336 135.6 24.2 64.433621636425215 84.084241442428336 27.3 84.084241442428336 138.19999999999999 141.80000000000001 11.52 53.95 55.76 Marzo MAR 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 126 140.5 208.2 65.900000000000006 112.1 114.78461812542623 68.5 244.1 92.1 87.959271881393278 114.78461812542623 101.8 114.7846181254262 3 88.5 95.2 80 129.69999999999999 81.209999999999994 Febrero FEB 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 107.8 25.4 262.5 67.3 103 85.596210863132185 85.596210863132185 85.596210863132185 85.596210863132185 60.074530357586383 85.596210863132185 68.5 85.596210863132185 42.5 124.3 6.06 106.38 53.34 MAR 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 126 140.5 208.2 65.900000000000006 112.1 114.78461812542623 68.5 244.1 92.1 87.959271881393278 114.78461812542623 101.8 114.78461812542623 88.5 95.2 80 129.69999999999999 81.209999999999994 abr Año ABR Salto 1982 87.8 1983 75.7 12.1 1984 16.3 59.4 1985 24.2 7.9 1986 73.8 49.5618086038 1987 73.8 0 1988 115.1 41.3381913962 1989 73.8 41.3381913962 1990 58.2 15.5618086038 1991 52.8 5.444679547 1992 154.4 101.644679547 1993 79.8 74.6 1994 73.8 6.0381913962 1995 64.8 8.9618086038 1996 54.5 10.3 1997 43.6 10.86 1998 135.2 91.52 1 2 1999 70.3 64.85 PERIODO 1982-1986 1987-1999 n datos 5 13 Promedio 55.6 80.8 S Des. Estandar 32.7915383321 33.4588207602 conprobacion de la varianza S2 Varianza 1075.2849861831 1119.4926866652 1075.2849861831 1119.4926866652 Sp = 33.2932539945 Sd = 17.5200692428 Tc = 1.4390970692 Tt = 2.1199052992 FC = 1.0411125432 Ft = 5.9117291091 Prueba t para dos muestras suponiendo varianzas iguales Variable 1 Variable 2 Media 80.7654420203 55.5523617208 Varianza 1119.4926866652 1075.2849861831 Observaciones 13 5 Varianza agrupada 1108.4407615447 Diferencia hipotética de las medias 0 Grados de libertad 16 Estadístico t 1.4390970692 P(T<=t) una cola 0.0846996513 Valor crítico de t (una cola) 1.7458836763 P(T<=t) dos colas 0.1693993026 Valor crítico de t (dos colas) 2.1199052992 Prueba F para varianzas de dos muestras Variable 1 Variable 2 Media 80.7654420203 55.5523617208 Varianza 1119.4926866652 1075.2849861831 Observaciones 13 5 Grados de libertad 12 4 F 1.0411125432 P(F<=f) una cola 0.5362381274 Valor crítico para F (una cola) 5.9117291091 Enero Enero 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 51.5 87.3 107.5 23.4 90.5 248.3 84.084241442428336
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