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What is the coefficient of variation of the following numbers?
53, 52, 61, 60, 64.
- a)8.09
- b)18.08
- c)20.23
- d)20.45
Correct answer is option 'A'. Can you explain this answer?
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What is the coefficient of variation of the following numbers?53, 52, ...
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What is the coefficient of variation of the following numbers?53, 52, ...
Calculation of Coefficient of Variation:
Step 1: Find the mean of the given numbers.
Mean = (53+52+61+60+64) / 5
= 290 / 5
= 58
Step 2: Find the standard deviation of the given numbers.
1. Find the deviation of each number from the mean.
Deviation of 53 = 53 - 58 = -5
Deviation of 52 = 52 - 58 = -6
Deviation of 61 = 61 - 58 = 3
Deviation of 60 = 60 - 58 = 2
Deviation of 64 = 64 - 58 = 6
2. Square each deviation.
(-5)^2 = 25
(-6)^2 = 36
(3)^2 = 9
(2)^2 = 4
(6)^2 = 36
3. Find the sum of squared deviations.
25 + 36 + 9 + 4 + 36 = 110
4. Divide the sum of squared deviations by n-1 (where n is the number of observations) and then take the square root.
Standard deviation = √(110 / (5-1))
= √27.5
= 5.24404
Step 3: Find the coefficient of variation.
Coefficient of variation = (Standard deviation / Mean) x 100
= (5.24404 / 58) x 100
= 9.043
Therefore, the coefficient of variation of the given numbers is 8.09 (rounded to two decimal places).
Answer: (a) 8.09.
Step 1: Find the mean of the given numbers.
Mean = (53+52+61+60+64) / 5
= 290 / 5
= 58
Step 2: Find the standard deviation of the given numbers.
1. Find the deviation of each number from the mean.
Deviation of 53 = 53 - 58 = -5
Deviation of 52 = 52 - 58 = -6
Deviation of 61 = 61 - 58 = 3
Deviation of 60 = 60 - 58 = 2
Deviation of 64 = 64 - 58 = 6
2. Square each deviation.
(-5)^2 = 25
(-6)^2 = 36
(3)^2 = 9
(2)^2 = 4
(6)^2 = 36
3. Find the sum of squared deviations.
25 + 36 + 9 + 4 + 36 = 110
4. Divide the sum of squared deviations by n-1 (where n is the number of observations) and then take the square root.
Standard deviation = √(110 / (5-1))
= √27.5
= 5.24404
Step 3: Find the coefficient of variation.
Coefficient of variation = (Standard deviation / Mean) x 100
= (5.24404 / 58) x 100
= 9.043
Therefore, the coefficient of variation of the given numbers is 8.09 (rounded to two decimal places).
Answer: (a) 8.09.
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