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.


Standard Deviation Problems

Variance Solution


2

Find the variance for the following series of numbers:

2, 3, 6, 8, 11.

Variance Operations

Variance Problems


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

Variance Operations

Variance Exercise


3

Find the variance for the series:

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

Variance Example

Variance

Variance Operations


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

Variance Solution

Variance

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 Operations

Variance

Variance Solution


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 Operations

Variance

Variance Solution


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

Variance Operations

2

Variance Exercise




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