Range of Data Set
The range is the difference between the largest and the smallest values in the distribution.
Thus, it can be written as
R = L – S
where,
L is the largest value in the Distribution
S is the smallest value in the Distribution
- A higher value of range implies higher variation in the data set.
- One drawback of this measure is that it only takes into account the maximum and the minimum value. They might not always be the proper indicator of how the values of the distribution are scattered.
Example: Find the range of the data set 10, 20, 15, 0, 100.
Solution:
- Smallest Value in the data = 0
- Largest Value in the data = 100
Thus, the range of the data set is,
R = 100 – 0
R = 100
Note: Range cannot be calculated for the open-ended frequency distributions. Open-ended frequency distributions are those distributions in which either the lower limit of the lowest class or the higher limit of the highest class is not defined.
Range for Ungrouped Data
To find the range for the ungrouped data set, first we have to find the smallest and the largest value of the data set by observing. The difference between them gives the range of ungrouped data.
We can understyand this with the help of following example:
Example: Find out the range for the following observations, 20, 24, 31, 17, 45, 39, 51, 61.
Solution:
- Largest Value = 61
- Smallest Value = 17
Thus, the range of the data set is
Range = 61 – 17 = 44
Range for Grouped Data
The range of the grouped data set is found by studying the following example,
Example: Find out the range for the following frequency distribution table for the marks scored by class 10 students.
| Marks Intervals | Number of Students |
|---|---|
| 0-10 | 5 |
| 10-20 | 8 |
| 20-30 | 15 |
| 30-40 | 9 |
Solution:
- For Largest Value: Taking the higher limit of Highest Class = 40
- For Smallest Value: Taking the lower limit of Lowest Class = 0
Range = 40 – 0
Thus, the range of the given data set is,
Range = 40
Measures of Dispersion | Types, Formula and Examples
Measures of Dispersion are used to represent the scattering of data. These are the numbers that show the various aspects of the data spread across various parameters.
Let’s learn about the measure of dispersion in statistics , its types, formulas, and examples in detail.
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