Question

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

• A. $\frac{\sqrt{52}}{7}$
• B. $\frac{52}{7}$
• C. $\frac{\sqrt{53}}{7}$
• D. $\frac{53}{7}$
• E. 6

Answer 1

Answer: (A)

Given data $6,5,9,13,12,8,10$
Mean of the given data$(\bar{x})$
$=\frac{6+5+9+13+12+8+10}{7}$
$=\frac{63}{7}=9$
The deviation of the respective data from the mean i.e. $\left(x_i-\bar{x}\right)$ are
$6-9,5-9,9-9,13-9,12-9,8-9,10-9$
$\left(x_i-\bar{x}\right)=-3,-4,0,4,3,-1,1$
${\left(x_i-\bar{x}\right)}^2=9,16,0,16,9,1,1$
$\sum _{i=1}^7{\left(x_i-\bar{x}\right)}^2=9+16+0+16+9+1+1$
$=52$
$\therefore$ Standard deviation $(\sigma )$
$=\sqrt{\frac{1}{n}\sum _{i=1}^7{\left(x_i-\bar{x}\right)}^2}=\sqrt{\frac{52}{7}}$