Question

The standard deviation of some temperature data in °C is 5. If the data were converted into ºF, the variance would be ______.

Options

• 81

• 57

• 36

• 25

Answer 1

The standard deviation of some temperature data in °C is 5. If the data were converted into ºF, the variance would be 81.

Explanation:

Given that `sigma_C` = 5

We know that C = `5/9(F - 32)`

⇒ F = `(9C)/5 + 32`

∴ `sigma_F = 9/5 sigma_C`

= `9/5 xx 5`

= 9

∴ `sigma_F^2 = (9)^2` = 81