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38
MCQ (Single Correct Answer)

If the coefficient of variation of two distributions are 50, 60 and their arithmetic means are 30 and 25 respectively, then the difference of their standard deviation is

A
0
B
1
C
1.5
D
2.5
39
MCQ (Single Correct Answer)

The standard deviation of some temperature data in ${ }^{\circ} \mathrm{C}$ is 5 . If the data were converted into ${ }^{\circ} \mathrm{F}$, then the variance would be

A
81
B
57
C
36
D
25
40

Coefficient of variation $=\frac{\cdots}{\text { Mean }} \times 100$

Explanation

$\text{CV}=\frac{S D}{\text { Mean }} \times 100$

41

If $\overline{\boldsymbol{x}}$ is the mean of $n$ values of $\boldsymbol{x}$, then $\sum_\limits{i=1}^n\left(\boldsymbol{x}_1-\overline{\boldsymbol{x}}\right)$ is always equal to .......... . If $a$ has any value other than $\overline{\boldsymbol{x}}$, then $\sum_\limits{i=1}^n\left(\boldsymbol{x}_i-\overline{\boldsymbol{x}}\right)^2$ is ................. than $\sum\left(x_i-a\right)^2$

Explanation

If $\bar{x}$ is the mean of $n$ values of $x$, then $\sum_\limits{i=1}^n\left(x_i-\bar{x}\right)=0$ and if a has any value other than $\bar{x}$, then $\sum_\limits{i=1}^n\left(x_i-\bar{x}\right)^2$ is less than $\sum\left(x_i-a\right)^2$.

42

If the variance of a data is 121 , then the standard deviation of the data is ............ .

Explanation

If the variance of a data is 121.

Then,

$$\begin{aligned} \mathrm{SD} & =\sqrt{\text { Variance }} \\ & =\sqrt{121}=11 \end{aligned}$$