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Question

The coefficient of variation of two distributions are 50% and 60%, and their arithmetic means are 30 and 25, respectively. The difference in their standard deviation is


A

1

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B

1.5

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C

2.5

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D

0

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Solution

The correct option is D

0


Explanation for the correct option:

Finding the difference between two standard deviations.

Given:

The coefficient of variance of first distribution be CV1=50

The coefficient of variance of second distribution be CV2=60

The arithmetic mean of first distribution be x1=30

The arithmetic mean of Second distribution be x2=25

We know that,

CV=σx×100 Where σ denotes the standard deviation, x denotes mean.

CV1=σ1x1×10050=σ130×100Givenσ1=30×50100=15

The standard deviation for the first distribution be σ1=15

similarly,

CV2=σ2x2×10060=σ225×100Givenσ2=60×25100=15

The standard deviation for the second distribution be σ2=15

Calculate the difference between two standard deviation:

σ1-σ2=15-15=0

Hence, Option(D) is the correct answer.


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