# Tyler played 5 games of basketball. The mean was 10 points. The median was 12 points. What might each of his scores be?

$0 , 0 , 12 , 19 , 19$ is one possibility

#### Explanation:

We have 5 basketball games where Tyler scored a mean of 10 points and a median of 12 points.

The median is the middle value, and so we know the points he scored have two values below 12 and two values above.

The mean is calculated by summing the values and dividing by the count. To have a mean of 10 points over 5 games, we know:

$\text{mean"="sum of points scored"/"number of games} \implies 10 = \frac{50}{5}$

And so the number of points scored over the 5 games is 50 points.

We know 12 was scored in one game, and so the remaining points will equal:

$50 - 12 = 38$, again, with two values above 12 and two below 12.

Let's make things easy and say that in the two games where he scored less than 12 points, he scored 0 points each. That leaves us with:

$38 - 2 \left(0\right) = 38$ for the remaining 2 games, and so he scored 19 in each of the other 2 games.

And so:

$0 , 0 , 12 , 19 , 19$

(In basketball, a basket is 2 points, but there are free throws that earn 1 each and 3-point shots that earn 3 points, so we can safely have odd numbers of points).