FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.45Measures of dispersion are mainly of two types–
(A) Absolute measures are as follows :
(i) Range, (ii) Mean deviation (or Average deviation), (iii) Standard deviation
(B) Among the Relative measures we find the following types :
(i) Coefficient of dispersion. (ii) Coefficient of variation.
5.3.2. Absolute and Relative measures :
If we calculate dispersion of a series, say, marks obtained by students in absolute figures, then dispersion will
be also in the same unit (i.e. marks). This is absolute dispersion. If again dispersion is calculated as a ratio (or
percentage) of the average, then it is relative dispersion.
5.3.2.1. RANGE :
For a set observations, range is the difference between the extremes, i.e.
Range = Maximum value – Minimum value
Illustration 43. The marks obtained by 6 students were 24, 12, 16, 11, 40, 42. Find the Range. If the highest
mark is omitted, find the percentage change in the range.
Here maximum mark = 42, minimum mark = 11.
∴ Range = 42 – 11 = 31 marks
If again the highest mark 42 is omitted, then amongst the remaining. Maximum mark is 40. So, range
(revised) = 40 – 11 = 29 marks.
Change in range = 31 – 29 = 2 marks.
∴ Reqd. percentage change = 2 ÷ 31 × 100 = 6.45%
Note : Range and other obsolute measures of dispersion are to be expressed in the same unit in which
observations are expressed.
For grouped frequency distribution :
In this case range is calculated by subtracting the lower limit of the lowest class interval from the upper
limit of the highest.
Example 44 : For the following data calculate range :
Marks Frequency
10–15 2
15–20 3
20–25 4
25–30 1Here upper limit of the highest class interval = 30
And lower limit of the first class interval = 10
∴ Range = 30 – 10 = 20 marks
Note : Alternative method is to subtract midpoint of the lowest class from that of the highest. In the above
case, range = 27.5 – 12.5 = 15 marks.
In practice both the methods are used.