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

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 will be

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

σ_F = 9²

=81

This is the required variance