Explanation
The Coefficient of Variation (C.V.) is a statistical measure of the relative dispersion of data points in a data series around the mean. The formula relating the Coefficient of Variation (C.V.), Standard Deviation (σ), and Arithmetic Mean (xˉ) is given by:
C.V.=(xˉσ)×100
Rearranging this formula to find the Arithmetic Mean (xˉ):
xˉ=(C.V.σ)×100
Step-by-Step Calculation
Step 1: Calculate the Arithmetic Mean for the First Distribution (xˉ1)
Using the rearranged formula:
xˉ1=(7515)×100
Simplify the fraction:
xˉ1=51×100
xˉ1=20
Step 2: Calculate the Arithmetic Mean for the Second Distribution (xˉ2)
Using the rearranged formula:
xˉ2=(8016)×100
Simplify the fraction:
xˉ2=51×100
xˉ2=20
Conclusion
The arithmetic means of both distributions are 20 and 20 respectively.
Correct Answer:
(c) 20 and 20.
