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Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, ...


Question

Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Options

A) 2

B) 3

C) \(\sqrt{10}\)

D) \(\sqrt{11}\)

The correct answer is C.

Explanation:

x = \(\frac{\sum x}{N}\)
= \(\frac{0}{11}\)
= 0
\(\begin{array}{c|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\)
= \(\sqrt{\frac{110}{11}}\)
= \(\sqrt{10}\)

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Dicussion (1)

  • x = \(\frac{\sum x}{N}\)
    = \(\frac{0}{11}\)
    = 0
    \(\begin{array}{c|c} x & (x - x) & (x - x)^2 \\\hline -5 & -5 & 25 \\ -4 & -4 & 16 \\-3 & -3 & 9 \\ -2 & -2 & 4 \\ -1 & -1 & 1\\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 2 & 4\\ 3 & 3 & 9\\ 4 & 4 & 16 \\5 & 5 & 25\\ \hline & & 110\end{array}\)
    S.D = \(\sqrt{\frac{\sum(x - x)^2}{\sum f}}\)
    = \(\sqrt{\frac{110}{11}}\)
    = \(\sqrt{10}\)

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