Question

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

• A. $$\sqrt{\frac{52}{7}}$$
• B. $$\frac{52}{7}$$
• C. $$\sqrt{6}$$
• D. 6

Answer 1

Answer:

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

Solution:

Given:

Given observation: 6, 5, 9, 13, 12, 8, 10

Concept used:

Standard deviation, $\sigma = \sqrt {\frac{\sum x^2_i}{n}-{(\frac{\sum x_i}{n})}^2}$

Calculation:

n = 7

$\sum \frac{x_i}{n} = \frac {6 + 5 + 9 + 13 + 12 + 8 + 10}{7}=9$

$\frac{\sum x^2_i}{n} = \frac {6^2 + 5^2 + 9^2 + 13^2 + 12^2 + 8^2 + 10^2}{7}=\frac{619}{7}$

Now, the standard deviation,

$\sqrt{\frac{619}{7}-9^4}$

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

∴ The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is  $\sqrt{\frac{52}{7}}$