The simplest measure of dispersion is the range, which is the difference between the maximum value and the minimum value of data.
Example 1: Find the range for the following three sets of data:
|
Set 1: |
05 |
15 |
15 |
05 |
15 |
05 |
15 |
15 |
15 |
15 |
|
Set 2: |
8 |
7 |
15 |
11 |
12 |
5 |
13 |
11 |
15 |
9 |
|
Set 3: |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
Solution:
In each of these three sets, the highest number is 15 and the lowest number is 5. Since the range is the difference between the maximum value and the minimum value of the data, it is 10 in each case.
But the range fails to give any idea about the dispersal or spread of the series between the highest and the lowest value. This becomes evident from the above data.
In a frequency distribution, range is calculated by taking the difference between the upper limit of the highest class and the lower limit of the lowest class.
Example 3.2: Find the range for the following frequency distribution:
|
Size of Item |
Frequency |
|
20- 40 |
7 |
|
40- 60 |
11 |
|
60- 80 |
30 |
|
80-100 |
17 |
|
100-120 |
5 |
|
Total |
70 |
Solution:
Here, the upper limit of the highest class is 120 and the lower limit of the lowest class is 20. Hence, the range is 120 - 20 = 100. Note that the range is not influenced by the frequencies. Symbolically, the range is calculated b the formula L - S, where L is the largest value and S is the smallest value in a distribution.
The coefficient of range is calculated by the formula: (L-S)/ (L+S). This is the relative measure. The coefficient of the range in respect of the earlier example having three sets of data is: 0.5.The coefficient of range is more appropriate for purposes of comparison as will be evident from the following example:
Example 3: Calculate the coefficient of range separately for the two sets of data
|
given below: |
|
|||||||
|
Set 1 |
8 |
10 |
20 |
9 |
15 |
10 |
13 |
28 |
|
Set 2 |
30 |
35 |
42 |
50 |
32 |
49 |
39 |
33 |
Solution: It can be seen that the range in both the sets of data is the same:
Set 1 28 - 8 = 20
Set 2 50 - 30 = 20
Coefficient of range in Set 1 is:
28 – 8 = 0.55
28+8
Coefficient of range in set 2 is:
50 – 30
50 +30 = 0.25
LIMITATIONS OF RANGE
There are some limitations of range, which are as follows:
- It is based only on two items and does not cover all the items in a
- It is subject to wide fluctuations from sample to sample based on the same
- It fails to give any idea about the pattern of distribution. This was evident from the data given in Examples 1 and 3.
- Finally, in the case of open-ended distributions, it is not possible to compute the
Despite these limitations of the range, it is mainly used in situations where one wants to quickly have some idea of the variability or' a set of data. When the sample size is very small, the range is considered quite adequate measure of the variability.
Thus, it is widely used in quality control where a continuous check on the variability of raw materials or finished products is needed. The range is also a suitable measure in weather forecast. The meteorological department uses the range by giving the maximum and the minimum temperatures. This information is quite useful to the common man, as he can know the extent of possible variation in the temperature on a particular day.