Question

find the variance of following data 12,22,28,24,21,16,31,14​

Answer 1

Step-by-step explanation:

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Answer 2

We need to recall the following formulas:

• Mean: $\bar x =\frac{\sum_{i=1}^{n}x }{n}$
• Variance : $\sigma^2=\frac{\sum_{i=1}^{n}(x_i - \bar x)^2 }{n}$

This problem is about variance.

Given:

$12,22,28,24,21,16,31,14$

There are total $8$ numbers in the given data.

The mean of the data is,

$\bar x =\frac{12+22+28+24+21+16+31+14 }{8}$

$\bar x =\frac{168 }{8}$

$\bar x =21$

The variance of the given data is,

$\sigma^2=\frac{\sum_{i=1}^{n}(x_i - \bar x)^2 }{n}$

$\sigma^2=\frac{(12-21)^2 +(22-21)^2+(28-21)^2+(24-21)^2+(21-21)^2+(16-21)^2+(31-21)^2+(14-21)^2}{8}$

$\sigma^2=\frac{(-9)^2 +(1)^2+(7)^2+(3)^2+(0)^2+(5)^2+(10)^2+(7)^2}{8}$

$\sigma^2=\frac{81+1+49+9+0+25+100+49}{8}$

$\sigma^2=\frac{314}{8}$

$\sigma^2=39.25$

Hence, the variance of given data is $39.25$.