Question

The standard deviation of some temperature data in degree Celsius (°C) is 5. If the data were converted into degree Fahrenheit (°F) then what is the variance?

Answer 1

Standard deviation (σ) = 5

Variance = 5² = 25

We know the formula, F = \(\frac{9}{5}\) C + 32

Variance (F) = Variance \(\frac{9}{5}\) C° + 32

[Variance of ax + b = a² (variance of x)]

= \((\frac{9}{5})^2\).variance

= \(\frac{81}{25}\) x 25

= 81° F

New variance = 81° F