Question on: JAMB Mathematics - 2014
Find the standard deviation of 5, 4, 3, 2, 1
A
\(\sqrt{2}\)
B
\(\sqrt{3}\)
C
\(\sqrt{6}\)
D
\(\sqrt{10}\)
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Correct Option: A
Mean x = \(\frac{\sum x}{n}\)
\( = \frac{5 + 4 + 3 + 2 + 1}{5}\)
\( = \frac{15}{5}\)
= 3
\(\begin{array}{c|c}
x & d = x - 3 & d^2 \\ \hline
5 & 2 & 4 \\ 4 & 1 & 1 \\ 3 & 0 & 0 \\ 2 & -1 & 1 \\ 1 & -2 & 4 \\ \hline
& & \sum d^2 + 10
\end{array}\)
Hence, standard deviation;
\( = \sqrt{\frac{\sum d^2}{n}} = \sqrt{\frac{10}{5}}\)
\( = \sqrt{2}\)
\( = \frac{5 + 4 + 3 + 2 + 1}{5}\)
\( = \frac{15}{5}\)
= 3
\(\begin{array}{c|c}
x & d = x - 3 & d^2 \\ \hline
5 & 2 & 4 \\ 4 & 1 & 1 \\ 3 & 0 & 0 \\ 2 & -1 & 1 \\ 1 & -2 & 4 \\ \hline
& & \sum d^2 + 10
\end{array}\)
Hence, standard deviation;
\( = \sqrt{\frac{\sum d^2}{n}} = \sqrt{\frac{10}{5}}\)
\( = \sqrt{2}\)
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