Question

The standard deviation of the scores $505,510 , 515,520, \ldots \ldots, 595$ is

• A. $500+5 \sqrt{30}$
• B. $505+\sqrt{30}$
• C. $5 \sqrt{30}$
• D. $5+\sqrt{30}$

Answer 1

Answer: (C)

Given, scores $505,510,515,520, \ldots 595$ the mean of these 19 scores $=550=\bar{x}$
So, $\displaystyle \sum_{i=1}^{19}\left(x_{i}-\bar{x}\right)^{2} =2\left(45^{2}+40^{2}+35^{2}+\ldots+5^{2}\right)$
$=2 \times 5^{2} \times\left[1^{2}+2^{2}+3^{2}+\ldots+9^{2}\right]$
So, standard derivation
$=\sqrt{\frac{\displaystyle \sum_{i=1}^{19}\left(x_{i}-\bar{x}\right)^{2}}{n}}$
$=\sqrt{\frac{2 \times 5^{2} \times \frac{9 \times 10 \times 19}{6}}{19}}$
$=5 \sqrt{30}$