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The coefficients of variations for the two distributions are 60 and 70 and its standard deviations are 21 and 16 respectively. Determine its arithmetic mean.

The coefficients of variations for the two distributions are 60 and 70 and its standard deviations are 21 and 16 respectively. Determine its arithmetic mean.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given that,

Coefficient of Variations (C.V of 1st distribution) = 60, σ1= 21

Coefficient of Variations (C.V of 2nd distribution) = 70, σ2= 16

Let μ1and μ2are the means of the 1st and the 2nd distribution.

We know that the formula to find the arithmetic mean is given as:

Coefficient of Variations(C.V) = (Standard Deviation/arithmetic Mean) x 100

Thus, Arithmetic Mean = (Standard Deviation/C.V)x100

Therefore, the arithmetic mean for the 1st deviation is given by:

μ1= [σ1/ (c.v of 1st distribution)]x100

μ1= (21/60)x100

μ1= 0.35×100

μ1= 35

Similarly for μ2:

μ2= [σ2/ (c.v of 2nd distribution)]x100

μ2= (16/70)x100

μ2= 0.2285×100

μ2= 22.85

Thanks

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