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

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 (fx square)
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