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Q.
The standard deviation of some temperature data in $^{\circ}C$ is 5. If the data were converted into $^{\circ}F$, the new variance would be _______
Statistics
Solution:
Given,$\sigma_{C}=5$
Relation between$^{\circ}C$ and $^{\circ}F$ is given by
$F=\frac{9C}{5}+32$
$\therefore \sigma_{F}=\frac{9}{5}\sigma_{C}=\frac{9}{5}\times5=9$
Here,$\sigma^{2}_{F}=\left(9\right)^{2}=81 $