The S.D. of scores 1, 2, 3, 4, 5 is: Options: A . &nbsp√2 B . &nbsp√3 C . &nbsp25 D . &nbsp35

Answer: Option A : A H e r e ¯ x = 1 + 2 + 3 + 4 + 5 5 = 3 x x − ¯ x ( x − ¯ x 2 ) 1 − 2 4 2 − 1 1 3 0 0 4 1 1 5 2 4 ∴ ∑ ( x − ¯ x ) 2 = 10 ∴ S . D = σ = √ ( x − ¯ x ) N = √ 10 5 = √ 2

The S.D. of scores 1, 2, 3, 4, 5 is:

Question

The S.D. of scores 1, 2, 3, 4, 5 is:

Options:

A . √2

B . √3

C . 25

D . 35

Answer: Option A
:
A

H e r e ¯ x = \frac{1 + 2 + 3 + 4 + 5}{5} = 3

\begin{matrix} x & x - ¯ x & (x - {¯ x}^{2}) 1 & - 2 & 4 2 & - 1 & 1 3 & 0 & 0 4 & 1 & 1 5 & 2 & 4 \end{matrix} ∴ \sum (x - ¯ x)^{2} = 10

∴ S . D = σ = \sqrt{\frac{(x - ¯ x)}{N}} = \sqrt{\frac{10}{5}} = \sqrt{2}

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