Find the SD of the following set of observations 45, 36, 40, 37, 39, 4

Find the SD of the following set of observations 45, 36, 40, 37, 39, 42, 45, 35, 40, 39.

Answer»

\(\bar x = \frac{\sum x_i}{n}\)

\(=\frac{45+36+40+37+39+42+45+35+40+35}{10}\)

\(=\frac{398}{10}=39.8\)

Now,

x_i	x_i - \(\bar{\text x}\)	(x_i - \(\bar{\text x}\))²
45	5.2	27.04
36	3.8	14.44
40	0.2	0.04
37	2.8	7.84
39	0.8	0.64
42	2.2	4.84
45	5.2	27.04
35	4.8	23.04
40	0.2	0.04
39	0.8	0.64
		\(\sum(x_i-\bar x)^2=105.6\)

\(\therefore \) Standard deviation is \(\sigma = \sqrt{\frac{\sum(x_i-\bar x)^2}{n-1}}\)

= \(\sqrt{\frac{105.6}9}\) = \(\sqrt{11.73}\) = 3.425

\(\therefore \) Standard deviation of given observation is 3.425

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Find the SD of the following set of observations 45, 36, 40, 37, 39, 42, 45, 35, 40, 39.

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