Question

What is the variance of the following series: 6, 2, 4, 7, 3, 2

a.
4.4

b.
3.4

c.
2.4

d.
1.4

Answer 1

Option b

Explanation:

Given : Series 6,2,4,7,3,2.

To find : What is the variance of the series?

Solution :

The variance formula is given by,

`\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}`

Step 1 - The mean of the series,

`\bar{x}=(6+2+4+7+3+2)/(6)`

`\bar{x}=(24)/(6)`

`\bar{x}=4`

Step 2 - Find
`\sum(x_i-\bar{x})^2`

`\sum(x_i-\bar{x})^2=(6-4)^2+(2-4)^2+(4-4)^2+(7-4)^2+(3-4)^2+(2-4)^2`

`\sum(x_i-\bar{x})^2=(2)^2+(-2)^2+(0)^2+(3)^2+(-1)^2+(-2)^2`

`\sum(x_i-\bar{x})^2=4+4+0+9+1+4`

`\sum(x_i-\bar{x})^2=22`

Step 3 - Substitute back in formula,

`\sigma^2=(22)/(6)`

`\sigma^2=3.6`

Therefore, The variance of the series is 3.6.

So, Approximately option b is correct.