# make the mean of 2 data sets the same

I am in the process of computing my student's final scores and for some reason I couldn't figure this step out:

If I have 2 data sets of scores in the range [0,40] but one data set has a different mean than the other, how can I make the mean the same for both data sets such that:

Those who got a 40 will still get a 40 and

The new scores will still be in the [0,40] range?

ok, imagine applying a linear transformation $f(x) = ax+b$ to your dataset $X_1, \ldots, X_n$ with mean $m$. The mean of the new set will be $am + b$. Let the fixed value (for you, 40) be denoted $u$, then you have to solve a system of two equations: $\mu = am + b$ (where $\mu$ is the desired new mean) and $u = au+b$.
Then, $a = \frac{u-\mu}{u-m}$, can you find $b$ and complete the problem?
• In your answer above, it should actually be $a=$ – Tomas Jorovic May 18 '15 at 18:44