Measures of dispersion; range, variance, mean deviation, standard deviation

The measures of dispersion is also called measure of variation.

The Range

The range is the simplest and most straight forward measure of dispersion.  It is the difference between the maximum values in the date.

Example

Find the range in the table below

Marks	6-10	11-15	16-20	21-25	26-30
Frequency	3	5	2	6	4

Solution

The maximum (highest) score = 30

The minimum (lowest) score = 6

= 24.

Mean Deviation

Examples:

Calculate the mean deviation for the set of data in table below

Age of SS2 students that won scholarship

	8	10	14	18
	4	3	5	8

Solution

Age of SS2 students that won scholarship

VARIANCE AND STANDARD DEVIATION

Example:  The marks scored by Economics Students in their NECO Examination are presented in the table below.  Calculate the variance and standard deviation.

Marks	10	20	30	40	50	60
No of students (frequency)	8	6	12	18	6	4

Questions

Marks scored by some  students in an economics test are;

6          9          5          7          6          7          5          8          9          5

8          9          5          7          5          8          7          8          6          5

6          5          7          6          9          9          7          8          8          7

8         9          8          5          8          9          5          6          9          7

8          5          6          9          8          6          7          6          9          5

2. Find the range of the grouped frequency table below.

X	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80
F	4	6	9	12	9	5	4	1