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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,

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

43

The standard deviation of a data is ........... of any change in origin but is ............. of change of scale.

Explanation

The standard deviation of a data is independent of any change in origin but is dependent of change of scale.