Question
Find the standard deviation of the first 21 natural numbers.
✓
Answer
Here $n =21$
The standard deviation of the first ' $n$ ' natural numbers,
$
\begin{aligned}
& =\sqrt{\frac{ n ^2-1}{12}} \\
& 1,2,3,4, \ldots, 21=\sqrt{\frac{21^2-1}{12}} \\
& =\sqrt{\frac{441-1}{12}} \\
& =\sqrt{\frac{440}{12}} \\
& =\sqrt{36.666} \\
& =\sqrt{36.67} \\
& =6.055 \\
& =6.06
\end{aligned}
$
The standard deviation of the first 21 natural numbers $=6.06$
The standard deviation of the first ' $n$ ' natural numbers,
$
\begin{aligned}
& =\sqrt{\frac{ n ^2-1}{12}} \\
& 1,2,3,4, \ldots, 21=\sqrt{\frac{21^2-1}{12}} \\
& =\sqrt{\frac{441-1}{12}} \\
& =\sqrt{\frac{440}{12}} \\
& =\sqrt{36.666} \\
& =\sqrt{36.67} \\
& =6.055 \\
& =6.06
\end{aligned}
$
The standard deviation of the first 21 natural numbers $=6.06$
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