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 correct option is D

$\sqrt{\frac{52}{7}}$

The given observations are 6,5,9,13,12,8,10

Now,

$\sum x_i$ = 6+5+9+13+12+8+10= 63

$\sum x_i^2$ = 36+25+81+169+144+64+100 = 619

$\therefore$ Standard deviation of the observations , $\sigma$

$=\sqrt{\frac{1}{N}\sum x_i^2-{(\frac{1}{N}\sum x_i)}^2}$

$=\sqrt{\frac{1}{7}\times 619-{(\frac{1}{7}\times 63)}^2}$

$=\sqrt{\frac{619}{7}-81}=\sqrt{\frac{619-567}{7}}=\sqrt{\frac{52}{7}}$

Hence, the correct answer is option (d).