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  • The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be A. 81 B. 57 C. 36 D. 25

The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be
A. 81
B. 57
C. 36
D. 25

Answers (1)

\\ \text{Given that the standard deviation of some temperature data in degree celcius, } \sigma _{c}=5 \\ \\ \text{We know that C}=\frac{5}{9} \left( F-32 \right) ~ F=\frac{9C}{5}+32~ \\ \\ \text{ Now we know that If S.D of x series is s, then S.D of kx series is ks. } \\ \\ \text{ So if SD of some temperature data is } \sigma _{c}=5 \\ \\ \text{Then SD of some temperature data in}\frac{9C}{5}~,\frac{9C}{5} \sigma _{c}=5 * \frac{9}{5}=9~ \\ \\ \text{Similarly, If SD of x series is s, then SD of k+x series is s}, \\
\\ \text{ So SD of some temperature data in}\frac{9C}{5}~ \sigma _{c}=9 \\ \\ \text{ And thus the SD of some temperature data in}\frac{9C}{5}+32 will be \sigma _{F}=\frac{9C}{5}~ \\ \\ ~ \sigma _{C}=9 \\ \\ \text{Now for variance, we will square on both sides, we get } \sigma _{F}=9^{2}=81 \\

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