Question
The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be:
- 81
- 57
- 36
- 25
The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be:
Solution:
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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