Question

In: Statistics and Probability

What is value of standard deviation of the 3-year moving average of Germany’s GDP from 1951...

What is value of standard deviation of the 3-year moving average of Germany’s GDP from 1951 to 1982? (Note: You should compare this value with the standard deviation of the original German GDP time series).

Unit 7 Homework Data
Age Systolic BP Year Stories Height Year Germany GDP
47 145 1990 54 770 1950 5.725433
65 162 1980 47 677 1951 6.256754
46 142 1990 28 428 1952 6.70308
67 170 1989 38 410 1953 7.256435
42 124 1966 29 371 1954 7.72644
67 158 1976 38 504 1955 8.570349
56 154 1974 80 1136 1956 9.076571
64 162 1991 52 695 1957 9.45931
56 150 1982 45 551 1958 9.665697
59 140 1986 40 550 1959 10.259906
34 110 1931 49 568 1960 10.608815
42 128 1979 33 504 1961 11.032132
48 130 1988 50 560 1962 11.384714
45 135 1973 40 512 1963 11.611703
17 114 1981 31 448 1964 12.266443
20 116 1983 40 538 1965 12.813883
19 124 1968 27 410 1966 13.016213
36 136 1927 31 409 1967 12.964814
50 142 1969 35 504 1968 13.730252
39 120 1988 57 777 1969 14.665157
21 120 1987 31 496 1970 15.392277
44 160 1960 26 386 1971 15.720841
53 158 1984 39 530 1972 16.197464
63 144 1976 25 360 1973 16.907173
29 130 1920 23 355 1974 16.97702
25 125 1931 102 1250 1975 16.72403
69 175 1989 72 802 1976 17.6721
1907 57 741 1977 18.195684
1988 54 739 1978 18.798212
1990 56 650 1979 19.640699
1973 45 592 1980 19.935295
1983 42 577 1981 19.903635
1971 36 500 1982 19.723139
1969 30 469 1983 19.985983
1971 22 320
1988 31 441
1989 52 845
1973 29 435
1987 34 435
1931 20 375
1931 33 364
1924 18 340
1931 23 375
1991 30 450
1973 38 529
1976 31 412
1990 62 722
1983 48 574
1984 29 498
1986 40 493
1986 30 379
1992 42 579
1973 36 458
1988 33 454
1979 72 952
1972 57 784
1930 34 476
1978 46 453
1978 30 440
1977 21 428

Solutions

Expert Solution

Year Germany GDP 3-year MA
1950 5.725433
1951 6.256754
1952 6.70308
1953 7.256435 6.22842233
1954 7.72644 6.73875633
1955 8.570349 7.22865167
1956 9.076571 7.85107467
1957 9.45931 8.45778667
1958 9.665697 9.03541
1959 10.25991 9.400526
1960 10.60882 9.794971
1961 11.03213 10.1781393
1962 11.38471 10.6336177
1963 11.6117 11.0085537
1964 12.26644 11.3428497
1965 12.81388 11.7542867
1966 13.01621 12.2306763
1967 12.96481 12.6988463
1968 13.73025 12.9316367
1969 14.66516 13.237093
1970 15.39228 13.786741
1971 15.72084 14.5958953
1972 16.19746 15.259425
1973 16.90717 15.770194
1974 16.97702 16.2751593
1975 16.72403 16.6938857
1976 17.6721 16.8694077
1977 18.19568 17.1243833
1978 18.79821 17.5306047
1979 19.6407 18.2219987
1980 19.9353 18.8781983
1981 19.90364 19.4580687
1982 19.72314 19.826543
1983 19.98598
sd 4.47684 4.02554558

Formula

Year Germany GDP 3-year MA
1950 5.725433
1951 6.256754
1952 6.70308
1953 7.256435 =AVERAGE(I2:I4)
1954 7.72644 =AVERAGE(I3:I5)
1955 8.570349 =AVERAGE(I4:I6)
1956 9.076571 =AVERAGE(I5:I7)
1957 9.45931 =AVERAGE(I6:I8)
1958 9.665697 =AVERAGE(I7:I9)
1959 10.259906 =AVERAGE(I8:I10)
1960 10.608815 =AVERAGE(I9:I11)
1961 11.032132 =AVERAGE(I10:I12)
1962 11.384714 =AVERAGE(I11:I13)
1963 11.611703 =AVERAGE(I12:I14)
1964 12.266443 =AVERAGE(I13:I15)
1965 12.813883 =AVERAGE(I14:I16)
1966 13.016213 =AVERAGE(I15:I17)
1967 12.964814 =AVERAGE(I16:I18)
1968 13.730252 =AVERAGE(I17:I19)
1969 14.665157 =AVERAGE(I18:I20)
1970 15.392277 =AVERAGE(I19:I21)
1971 15.720841 =AVERAGE(I20:I22)
1972 16.197464 =AVERAGE(I21:I23)
1973 16.907173 =AVERAGE(I22:I24)
1974 16.97702 =AVERAGE(I23:I25)
1975 16.72403 =AVERAGE(I24:I26)
1976 17.6721 =AVERAGE(I25:I27)
1977 18.195684 =AVERAGE(I26:I28)
1978 18.798212 =AVERAGE(I27:I29)
1979 19.640699 =AVERAGE(I28:I30)
1980 19.935295 =AVERAGE(I29:I31)
1981 19.903635 =AVERAGE(I30:I32)
1982 19.723139 =AVERAGE(I31:I33)
1983 19.985983
sd =STDEV(I2:I35) =STDEV(J5:J34)

sd for moving average =

4.02554558

sd for original data =

4.47684

sd in moving average is less than that of original data

orchestra answered 2 years ago
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