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

A.

√6

B.

√10

C.

√\(\frac{2}{5}\)

D.

√\(\frac{5}{2}\)

Correct answer is D

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

= \(\frac{16}{4}\)

= 4

S = \(\sqrt{\frac {(x - \bar{x})^2}{N}}\)

= \(\sqrt{\frac {(10)}{4}}\)

= \(\sqrt{\frac {(5)}{2}}\)