Question

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is 

A. 6 

B. \(\sqrt {6}\) 

C.  \(\frac{52}{7}\) 

D. \(\sqrt{\frac{52}{7}}\) 

Answer 1

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is 

xi	x2i
6	36
5	25
9	81
13	169
12	144
8	64
10	100
Σxi = 63	Σxi = 619

And, N=7

Standard deviation σ  = \(\sqrt{\Big(\frac{\Sigma x^2_i}{N} - \Big(\frac{\Sigma x_i}{N}\Big)^2\Big)}\) 

\(\sigma =\sqrt{\Big(\frac{619}{7} - \Big(\frac{63}{7}\Big)^2\Big)}\)

\(\sigma = \sqrt{\Big(\frac{7\times619\times3969}{49}\Big)}\) 

\(\sigma = \sqrt{\frac{396}{49}}\)  

\(\sigma = \sqrt{\frac{52}{7}}\)