First slide

Introduction to statistics

Question

The standard deviation of some temperature data in ^oC is 5. If the data were converted into ^oF, the new variance would be

Moderate

A

81
B

57
C

36
D

25

Solution

$Given, σ_{C} = 5$
${Relation between}^{\circ} C {and}^{\circ} F is given by$
$\begin{array}{l} F = \frac{9 C}{5} + 32 \\ ∴ σ_{F} = \frac{9}{5} σ_{C} = \frac{9}{5} \times 5 = 9 \\ Here, σ_{F}^{2} = (9)^{2} = 81 \end{array}$

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