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

MCQ

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

✓
$\sqrt{\frac{52}{7}}$
B
$\frac{52}{7}$
C
$\sqrt{6}$
D
$6$

✓

Answer

Correct option: A.

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

$\sqrt{\frac{52}{7}}$
Given data are $6, 5, 9, 13, 12, 8$ and $10$

$x_i$	$x_i^2$
$6$	$36$
$5$	$25$
$9$	$81$
$13$	$169$
$12$	$144$
$8$	$64$
$10$	$100$
$\sum\text{x}_\text{i}=63$	$\sum\text{x}_\text{i}^2=619$

$\therefore\ \text{SD}=\sigma=\sqrt{\frac{\sum\text{x}_\text{i}^2}{\text{N}}-\Big(\frac{\sum\text{x}_\text{i}}{\text{N}}\Big)^2}$
$=\sqrt{\frac{619}{7}-\Big(\frac{63}{7}\Big)^2}=\sqrt{\frac{4333-396}{49}}$
$=\sqrt{\frac{396}{49}}=\sqrt{\frac{52}{7}}$

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