Acetate 2

MEASURES OF DISPERSION

Range

The range tells us over how many numbers altogether a distribution is spread. It is calculated by subtracting the smallest score from the largest score e.g if we took an example of prices of apples in greengrocers' shops

10p,25p,12p,8p,14p,14p,24p,15p

Add 1 to the difference to account for possible measurement error

Semi-Interquartile Range

The range of the middle half of the scores. In certain circumstances the semi-interquartile range is a more stable measure of dispersion than the range.

The way of calculating the semi-interquartile range is by placing all the values in order, find the midpoint(y), then halve again to get (x) and (z) which gives 4 equal groups. Then subtract (z-x) and then divide by 2 to obtain the interquartile range. Work out the interquartile range for the following set of numbers

36,32,24,68,58,16,18,10,30,36,42

Mean Deviation

The mean deviation is a number which indicates how much on average the scores in a distribution differ from a central point, the mean. The way of calculating the mean deviation of a set of numbers is by putting the numbers into value order. Working out the mean for the set of numbers. For each number in the set work out the difference between the number and the mean. Add all the differences up and divide by the number of numbers in the group, this will give the mean deviation.

Work out the mean deviation for the following set of numbers

8,10,9,11,12

Variance

The variance is found immediately prior to the standard deviation and is often used as a measure of spread(and with ANOVA Analysis of Variance)

The way of calculating the variance of a set of numbers is by squaring all the numbers in the group, then add the numbers this will give you a figure called the sum of squares find out the mean of the sum of squares by dividing the sum of squares by the number of numbers in the group. The mean of the sum of squares is also known as the variance.

Work out the variance for the following set of numbers

-2,-1,0,+1,+2

Standard Deviation

The standard deviation is similar to mean deviation. It summarises an average distance of all the scores from the mean of a particular set but is calculated differently.

The way of calculating the standard deviation (S.D) of a set of numbers is by squaring all the numbers in the group, then add the numbers this will give you a figure called the sum of squares find out the mean of the sum of squares by dividing the sum of squares by the number of numbers in the group. The mean of the sum of squares is also known as the variance.

The standard deviation is the square root of the variance

Work out the standard deviation for the following set of numbers

-2,-1,0,+1,+2