Variance Problems

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