# Variance Problems

### Solutions

1Find the variance and standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.

2Find the variance for the following series of numbers:

2, 3, 6, 8, 11.

12, 6, 7, 3, 15, 10, 18, 5.

3Find the variance for the series:

3, 5, 2, 7, 6, 4, 9.

3, 5, 2, 7, 6, 4, 9, 1.

4Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate the variance.

5A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate the variance.

6 Consider the following data: 3, 8, 4, 10, 6, 2.

1. Calculate its mean and variance.

2. If all the above data was multiplied by 3, what would the new mean and variance be?

## 1

Find the variance and standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.  ## 2

Find the variance for the following series of numbers:

2, 3, 6, 8, 11.  12, 6, 7, 3, 15, 10, 18, 5.  ## 3

Find the variance for the series:

3, 5, 2, 7, 6, 4, 9. #### Variance 3, 5, 2, 7, 6, 4, 9, 1. #### Variance ## 4

Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate the variance.

 xi fi xi · fi xi2 · fi 61 5 305 18 065 64 18 1152 73 728 67 42 2814 188 538 71 27 1890 132 300 73 8 584 42 632 100 6745 455 803 #### Variance ## 5

A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate the variance.

 xi fi xi · fi xi2 · fi [10, 15) 12.5 3 37.5 468.75 [15, 20) 17.5 5 87.5 1537.3 [20, 25) 22.5 7 157.5 3543.8 [25, 30) 27.5 4 110 3025 [30, 35) 32.5 2 65 2112.5 21 457.5 10681.25 #### Variance ## 6

Consider the following data: 3, 8, 4, 10, 6, 2.

1. Calculate its mean and variance.

2. If all the above data was multiplied by 3, what would the new mean and variance be?

 xi xi2 2 4 3 9 4 16 6 36 8 64 10 100 33 229

#### 1 #### 2 