The standard deviation of the scores 505, 510, $515,520, \ldots \ldots ., 595$ is
The standard deviation of the scores 505, 510, $515,520, \ldots \ldots ., 595$ is
- $500+5 \sqrt{30}$
- $505+\sqrt{30}$
- $5 \sqrt{30}$
- $5+\sqrt{30}$
Solution
Given, scores 505, 510, 515, 520, ... 595 the mean of these 19 scores $=550=\bar{X}$
So,
$
\begin{aligned}
\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]
\end{aligned}
$
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}
$
Asked in: AP EAMCET 2018 (23 Apr Shift 2)
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