Choose the correct answer. The standard deviation of some tempera… - Vidyadip

MCQ

Choose the correct answer. The standard deviation of some temperature data in $^\circ C$ is $5.$ If the data were converted into $^\circ F,$ the variance would be:

✓
$81$
B
$57$
C
$27$
D
$36$

✓

Answer

Correct option: A.

$81$

Given that $\sigma_\text{c}=5$
We know that $\text{C}=\frac{5}{9}(\text{F}-32)$
$\Rightarrow\text{F}=\frac{9\text{C}}{5}+32$
$\therefore\ \sigma_\text{F}=\frac{9}{5}\sigma_\text{c}=\frac{9}{5}\times5=9$
$\therefore\ \sigma^2_{\text{F}}=(9)^2=81$

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