Calculation of Range and Coefficient of Range
Range and Coefficient of Range can be calculated in three different series:
(I) Individual Series
Example 1:
The salaries of 8 factory employees are listed below. Calculate the range and the coefficient of the range. The following salaries are in Indian rupees:
1400, 1450, 1520, 1380, 1485, 1495, 1575, and 1440.
Solution:
In ascending order, the wages are 1380, 1400, 1440, 1450, 1485, 1495, 1520, 1575
From the given values of salary, the Largest Item (L) = 1575, and the Smallest Item (S) = 1380
Range = L- S
= 1575 – 1380
Range = 195
Coefficient of Range = 0.065
Example 2:
Find the range and coefficient of the range of the following data:
43.1, 13.6, 18.5, 38.1, 61.4, 29.3
Solution:
In ascending order, the values are: 13.6, 18.5, 29.3, 38.1, 43.1, 61.4
Here, L = Largest Value; i.e., 61.4, S = Smallest Value;i.e., 13.6
Range = L – S
= 61.4 – 13.6
Range = 47.8
Coefficient of Range = 0.64
(II) Discrete Series
The values of the largest (L) and smallest (S) items in a discrete series should not be confused with the largest and smallest frequencies. They represent the largest and smallest values of the variable. Therefore, the range is determined without taking into account their frequencies by subtracting the smallest item from the largest item.
Example 1:
The number of homes and the number of people per home are shown in the distribution below. Find the range and coefficient of the range of the following distribution:
Solution:
Range (R) = Largest Item (L) – Smallest Item (S)
= 8 -1
Range = 7
Coefficient of Range = 0.77
Example 2:
The number of workers and production per day is shown in the distribution below. Find the range and coefficient of the range of the following distribution:
Solution:
Range = L – S
Here, L = Largest Value; i.e., 250 S = Smallest Value; i.e., 150
= 250 – 150
Range = 100
Coefficient of Range = 0.25
(III) Continuous Series
There are two ways to compute the range and coefficient of range for continuous frequency distributions:
1. First Method: Calculate the difference between the lower limits of the lowest-class interval and the upper limit of the highest-class interval.
2. Second Method: Calculate the difference between the mid-points of the lowest-class interval and the highest-class interval.
Note: Both methods will provide different results. However, both answers will be accurate.
Example 1:
The following data represents the weight of students in kg. Find the range and coefficient of the range using both methods.
Solution:
Range and Coefficient of Range by the First Method:
Range (R) = Largest Item (L) – Smallest Item (S)
= 62 – 50
Range = 12
Coefficient of Range = 0.107
Range and Coefficient of Range by the Second Method:
Range (R) = Mid-point of the Highest Class – Mid-point of the Lowest Class
= 61 – 51
Range = 10
Coefficient of Range= 0.089
Example 2:
Find the range and coefficient of range of the following series:
Solution:
In the above table, an inclusive series of marks and the number of students are given. First of all, the inclusive series will be converted into the exclusive series, after that, the largest and smallest value of the exclusive series of marks will be utilised to calculate the range and coefficient of range.
Range and Coefficient of Range by the First Method:
Range = L – S
Here, L = Largest value; i.e., 49.5, S = Smallest value; i.e., 9.5
Range = 49.5 – 9.5
Range = 40
Coefficient of Range = 0.67
Range and Coefficient of Range by the Second Method:
Range (R) = Mid-points of the Highest Class – Mid-points of the Lowest Class
= 44.5 – 14.5
Range = 30
Coefficient of Range = 0.51
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