# Find the Mean, Variance and Standard Deviation for the Data: 6, 7, 10, 12, 13, 4, 8, 12. - Mathematics

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

#### Solution

6,7,10,12,13,4,8,12

$\text{ Mean } = \frac{6 + 7 + 10 + 12 + 13 + 4 + 8 + 12}{8}$

$= \frac{72}{8}$

$= 9$

$x_i$
$\left( x_i - X \right) = \left( x_i - 9 \right)$

$\left( x_i - X \right)^2$
6 -3 9
7 -2 4
10 1 1
12 3 9
13 4 16
4

- 5
25
8

-1
1
12 3 9

$\sum^8_{i = 1} \left( x_i - X \right)^2 = 74$

n = 8

$\therefore \text{ Variance } \left( X \right) = \frac{\sum^8_{i = 1} \left( x_i - X \right)^2}{n}$

$= \frac{74}{8}$

$= 9 . 25$

$\text{ Standard deviation }= \sqrt{\text{Variance} \left( X \right)}$

$= \sqrt{9 . 25}$

$= 3 . 04$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.4 | Q 1.2 | Page 28