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Find the standard deviation of 2, 3, 5 and 6


Question

Find the standard deviation of 2, 3, 5 and 6

Options

A) √6

B) √10

C) √\(\frac{2}{5}\)

D) √\(\frac{5}{2}\)

The correct answer is D.

Explanation:

\(\begin{array}& x & x - \bar{x} & (x - \bar{x})^2 \\2 & -2 & 4 \\ 3 & -1 & 1 \\ 5 & 1 & 1 \\ 6 & 2 & 4\\ \hline \sum x = 16 & & \sum (x - \bar{x}^2) = 0 \end{array}\)
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\(\bar{x}\) = \(\frac{\sum x }{N}\)
= \(\frac{16}{4}\)
= 4
S = \(\sqrt{\frac {(x - \bar{x})^2}{N}}\)
= \(\sqrt{\frac {(10)}{4}}\)
= \(\sqrt{\frac {(5)}{2}}\)

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Dicussion (1)

  • \(\begin{array}& x & x - \bar{x} & (x - \bar{x})^2 \\2 & -2 & 4 \\ 3 & -1 & 1 \\ 5 & 1 & 1 \\ 6 & 2 & 4\\ \hline \sum x = 16 & & \sum (x - \bar{x}^2) = 0 \end{array}\)
    ___________________________________
    \(\bar{x}\) = \(\frac{\sum x }{N}\)
    = \(\frac{16}{4}\)
    = 4
    S = \(\sqrt{\frac {(x - \bar{x})^2}{N}}\)
    = \(\sqrt{\frac {(10)}{4}}\)
    = \(\sqrt{\frac {(5)}{2}}\)