Question

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).

a. 4.24 b. 4.33 c. 4.41 d. 4.56 e. 4.69

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

Answer 1

Have a look at the Germany GDP data-

Year	German GDP
1950	5.725433
1951	6.256754
1952	6.70308
1953	7.256435
1954	7.72644
1955	8.570349
1956	9.076571
1957	9.45931
1958	9.665697
1959	10.259906
1960	10.608815
1961	11.032132
1962	11.384714
1963	11.611703
1964	12.266443
1965	12.813883
1966	13.016213
1967	12.964814
1968	13.730252
1969	14.665157
1970	15.392277
1971	15.720841
1972	16.197464
1973	16.907173
1974	16.97702
1975	16.72403
1976	17.6721
1977	18.195684
1978	18.798212
1979	19.640699
1980	19.935295
1981	19.903635
1982	19.723139
1983	19.985983

The Standard Deviation can be found out in two ways-

a) Traditional Method:

Mean = Average of the Data

= (5.27+6.25+....+19.72+19.98)/34 = 13.42

Standard Deviation = { (5.27-13.42)^2 + (6.25-13.42)^2 + ... + (19.72-13.42)^2 + (19.98-13.42)^2 }/34

= 4.41

b) Using Excel:

Use the function Stdev.p(5.27:19.98) = 4.41

That will be Option- (c)

Let me know if you need anything else, if not please don't forget to like the answer :)