Question

According to the National Bureau of Economic Research, the lengths of business cycles from 1919 to 1995, measured from trough to trough (a trough is the low point) in months, were 61 38 46 50 74 73 98 58 65 44 127 62 74 38 110 57 Find the Standard Deviation, mean, median, mode, and midrange

Answer 1

(a)

Mean () is got as follows:

So,

Mean = 67.1875

(b)

x	(x - )	(x - )2
61	- 6.1875	38.2852
38	- 29.1875	851.9102
46	- 21.1875	448.9106
50	- 17.1875	295.4102
74	6.8125	46.4106
73	5.8125	33.7852
98	30.8125	949.4102
58	-9.1875	84.4102
65	- 2.1875	4.7852
44	- 23.1875	537.6602
127	59.8125	3577.5351
62	- 5.1875	26.9102
74	6.8125	46.4102
38	- 29.1875	851.9102
110	42.8125	1832.9102
57	- 10.1875	103.7852
Total =		9730.4375

Standard Deviation (s) is got as follows:

So,

Standard Deviation = 25.4695

(c)

Arranging data in ascending order, we get:

38, 38, 44, 46, 50,57, 58, 61, 62, 65, 73, 74, 74, 98, 110, 127

n = 16

Median is (16 + 1)/2th item = Average of 8th & 9th items= (61 + 62)/2 = 61.5

So,

Median = 61.5

(d)

Mode = 38 and 74

since 38 & 74 occur maximum number of times

(e)

Midrange = (127 + 38)/2 = 82.5

So,

Midrange = 82.5