Question

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

Answer 1

Given the standard deviation of some temperature data in °C, σ_C=5

We know that

Now we know

If standard deviation of x series is s, then standard deviation of kx series is ks,

So standard deviation of some temperature data in °C, σ_C=5,

And hence the standard deviation of some temperature data in

Similarly,

If standard deviation of x series is s, then standard deviation of k+x series is s,

So standard deviation of some temperature data in

And hence the standard deviation of some temperature data in 9C/5 + 32 will be

Now for variance, we will square on both sides, we get

σ_F = 9²

= 81

This is the required variance