Question

The standard deviation is equal to the square root of the average squared deviations about the mean. More succintly, it is equal to the square root of the variance. So one way to calculate the standard deviation of a frequency distribution is to calculate the variance. Complete the table below as the first step in calculating the variance:

(10 points)

X	f	X−x	(X−x)2
96	1
94	1
92	1
87	1
85	1
84	1
83	1
82	1
79	1
78	1
76	1
73	1
72	1
69	2
67	2
66	1
63	1
62	1
61	2
51	1
44	1
42	1

Answer 1

Solution-:

We prepare following table by using MS-Excel :

x	f	fi*xi	(x-xbar)	(x-xbar)^2	fi*(x-xbar)^2	fi*xi^2
96	1	96	23.88	570.2544	570.25	9216
94	1	94	21.88	478.7344	478.73	8836
92	1	92	19.88	395.2144	395.21	8464
87	1	87	14.88	221.4144	221.41	7569
85	1	85	12.88	165.8944	165.89	7225
84	1	84	11.88	141.1344	141.13	7056
83	1	83	10.88	118.3744	118.37	6889
82	1	82	9.88	97.6144	97.61	6724
79	1	79	6.88	47.3344	47.33	6241
78	1	78	5.88	34.5744	34.57	6084
76	1	76	3.88	15.0544	15.05	5776
73	1	73	0.88	0.7744	0.77	5329
72	1	72	-0.12	0.0144	0.01	5184
69	2	138	-3.12	9.7344	19.47	9522
67	2	134	-5.12	26.2144	52.43	8978
66	1	66	-6.12	37.4544	37.45	4356
63	1	63	-9.12	83.1744	83.17	3969
62	1	62	-10.12	102.4144	102.41	3844
61	2	122	-11.12	123.6544	247.31	7442
51	1	51	-21.12	446.0544	446.05	2601
44	1	44	-28.12	790.7344	790.73	1936
42	1	42	-30.12	907.2144	907.21	1764
Total	25	1803			4972.64	135005

From this table we get,

and

The standard deviation is equal to the square root of the average squared deviations about the mean.

Or

it is equal to the square root of the variance.