Question

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

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

Answer 1

Answer: (C)

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