Thursday, July 7, 2011

MEASURE OF CENTRAL TENDENCY ( STANDARD DEVIATION AND VARIANCE) FOR STATISTICS O LEVEL/IGCSE

The variance of a set of observations is defined as the mean of the square of deviations of all the observations from their mean.

Ungrouped formula

Variance = (∑x/n)-(∑x/n)

Frequency Distribution ( grouped )

Variance = (∑ƒx/∑ƒ) – (∑ƒx/∑ƒ)

And the standard deviation or S.D is the square root of the variance

SD=under root of variance

Example: find the variance and S.D of the following set of numbers

1, 3,1,3,4

x

x

1

1

3

9

1

1

3

9

4

16

∑x =12

∑x = 36

Variance= (∑x/n)-(∑x/n)

Variance=(36/5)-(12/5)

Variance=1.44

SD= under root of 1.44

SD=1.2

Example for frequency distribution

Class limits (in miles)

No of employees

X

fx

fx

1 – 3

10

2

20

400

4 – 6

14

5

70

4900

7 – 9

10

8

80

6400

10 – 12

6

11

66

4356

13 – 15

5

14

70

4900

16 – 18

5

17

85

7225

F=50

fx=391

fx=28181

Variance = (∑ƒx/∑ƒ) – (∑ƒx/∑ƒ)

Variance=(28181/50)-(391/50)

Variance= 502.47

SD=under root of 502.47

SD=22.42

No comments:

Post a Comment