Find the range and coefficient of range of the following data.(i) 63, 89, 98, 125, 79, 108, 117, 68(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
Question
Find the range and coefficient of range of the following data.
(i)
63, 89, 98, 125, 79, 108, 117, 68
(ii)
43.5, 13.6, 18.9, 38.4, 61.4, 29.8
Solution
Sure, let's find the range and coefficient of range for the given data sets.
(i) 63, 89, 98, 125, 79, 108, 117, 68
Step 1: Arrange the data in ascending order: 63, 68, 79, 89, 98, 108, 117, 125
Step 2: Find the range. The range is the difference between the highest and lowest values. So, Range = Highest value - Lowest value = 125 - 63 = 62
Step 3: Find the coefficient of range. The coefficient of range is calculated as (Highest value - Lowest value) / (Highest value + Lowest value). So, Coefficient of Range = Range / (Highest value + Lowest value) = 62 / (125 + 63) = 62 / 188 = 0.3298
(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
Step 1: Arrange the data in ascending order: 13.6, 18.9, 29.8, 38.4, 43.5, 61.4
Step 2: Find the range. The range is the difference between the highest and lowest values. So, Range = Highest value - Lowest value = 61.4 - 13.6 = 47.8
Step 3: Find the coefficient of range. The coefficient of range is calculated as (Highest value - Lowest value) / (Highest value + Lowest value). So, Coefficient of Range = Range / (Highest value + Lowest value) = 47.8 / (61.4 + 13.6) = 47.8 / 75 = 0.6373
So, the range and coefficient of range for the first data set are 62 and 0.3298 respectively, and for the second data set are 47.8 and 0.6373 respectively.
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