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  • Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is A. 0 B. 1 C. 1.5 D. 2.5

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
A. 0
B. 1
C. 1.5
D. 2.5

Answers (1)

\\ \text{Given coefficient of variation of two distributions are C}V_{1}=50 and CV_{2}=60 \\ \\ \text{ And the arithmetic means are }\overline{x_{1}}=30, \overline{x_{2}}=25~ \\ \\ \text{We know that coefficient of variation can be written as CV}= \frac{ \sigma }{\overline{x~}} * 100~ \\ \\ \text{Now for first distribution, we have C}V_{1}= \frac{ \sigma _{1}}{\overline{x_{1}~}} * 100 \\ \\ \text{Substituting corresponding values, we get 50}= \frac{ \sigma _{1}}{30} * 100 \\ \\ ~ \sigma _{1}=15 \ldots \ldots . \left( i \right) ~~ \\ \\ \text{ Now for second distribution, we have C}V_{2}= \frac{ \sigma _{2}}{\overline{x_{2}~}} * 100~ \\
\\ \text{Substituting corresponding values, we get 60}= \frac{ \sigma _{2}}{25} * 100 \\ \\ ~ \sigma _{2}=15 \ldots \ldots . \left( ii \right) ~~~ \\ \\ \text{So from both the equations we get that the difference of their standard deviation is 0 } \\

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