Measure Of Dispersion

A measure of dispersion is a method of measuring the degree by which numerical data or values tend to spread from or cluster about central point of average.

The most common measures of dispersion are the following

1.  The Range

• The simplest measure of dispersion.
• Calculated by finding the difference between the greatest and the least values of the data.
• Useful since it is the easiest to understand.
• Affected by extreme data.
• The range of values 1, 2, 4, 6, 9, 11, 15, 25 is 25 – 1 = 24

Ungrouped:

            R = H – L

= UB – LB

= 89.5 – 44.5

= 45

Grouped Data:

            R = UB – LB = Boundaries

Class Intervals	Frequency	Class Boundaries	Class Marks
45 – 49	3	44.5 + 49.5/2	47
50 – 54	4	49.5 + 54.5/2	52
55 – 59	6	54.5 + 59.5/2	57
60 – 64	7	59.5 + 64.5/2	62
65 – 69	10	64.5 + 69.5/2	67
70 – 74	7	69.5 + 74.5/2	72
75 – 79	6	74.5 + 79.5/2	77
80 – 84	4	79.5 + 84.5/2	82
85 – 89	3	84.5 + 89.5/2	87

Measure Of Dispersion (Cont.)  2.    The Quartile Deviation


Measure Of Dispersion (Cont.)  3.    The Standard Deviation