First slide

Introduction to statistics

Question

The standard deviation of the data 6, 5,9, 13, 12,8,10 is

Easy

A

$\sqrt{\frac{52}{7}}$
B

$\frac{52}{7}$
C

$\sqrt{6}$
D

$6$

Solution

Given, numbers are: 6, 5, 9, 13, 12, 8, 10
$x_{i}$ $x_{i}^{2}$
6 36
5 25
9 81
13 169
12 144
8 64
10 100
${Σx}_{i} = 63$ ${Σx}_{i}^{2} = 619$
$\begin{array}{l} ∴ S.D. = σ = \sqrt{\frac{{Σx}_{i}^{2}}{N} - {(\frac{{Σx}_{i}}{N})}^{2}} = \sqrt{\frac{619}{7} - {(\frac{63}{7})}^{2}} \\ = \sqrt{\frac{7 \times 619 - 3969}{49}} = \sqrt{\frac{4333 - 3969}{49}} \\ = \sqrt{\frac{364}{49}} = \sqrt{\frac{52}{7}} \end{array}$

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