The standard deviation of the numbers 22, $26,28,20,24,30$ is
The standard deviation of the numbers 22, $26,28,20,24,30$ is
- 2
- 2.4
- 3.24
- 3.42
Solution
Given numbers 22, 26, 28, 20, 24, 30
$
\bar{x}=\frac{22+26+28+20+24+30}{6}=\frac{150}{6}=25
$
Now, $\left(x_i-\bar{x}\right)^2$ is $9,1,9,25,1,25$
$
\begin{aligned}
& \text { Now, } S D=\sqrt{\frac{\Sigma\left(x_i-\bar{x}\right)^2}{n}} \\
& =\sqrt{\frac{9+1+9+25+1+25}{6}}=\sqrt{\frac{70}{6}}=3.42
\end{aligned}
$
Asked in: AP EAMCET 2018 (23 Apr Shift 1)
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