6.6 Measures of Dispersion
(A) Determine the range of a set of data
1. For an ungrouped data,
Range = largest value – smallest value.
2. For a grouped data,
Range = midpoint of the last class – midpoint of the first class.
Example 1:
Determine the range of the following data.
(a) 720, 840, 610, 980, 900
(b)
Time (minutes) |
1 – 6 |
7 – 12 |
13 – 18 |
19 – 24 |
25 – 30 |
Frequency |
3 |
5 |
9 |
4 |
4 |
Solution:
(a)
Largest value of the data = 980
Smallest value of data = 610
Range = 980 – 610 = 370
(b)
Midpoint of the last class
= ½ (25 + 30) minutes
= 27.5 minute
Midpoint of the first class
= ½ (1 + 6) minutes
= 3.5 minute
Range = (27.5 – 3.5) minute = 24 minutes