### Video Transcript

At a school, every student belongs
to one of four houses, and the houses compete throughout the year to earn
points. The graph shows how many points
each house had scored at the end of the year. Calculate the mean number of points
earned. Describe what the mean
represents.

We’re first asked to calculate the
mean number of points earned. The mean of a data set is found by
dividing the sum of all the values in the data set by how many values there are. Here, that means we need to divide
the total number of points earned by the number of houses.

We know that the number of houses
is four. To determine the total number of
points earned, we need to use the graph. Reading across to the vertical
axis, we see that the blue house earned 30 points. The orange house earned 70
points. The pink and green houses earned 50
and 90 points, respectively. The total of these four values is
240. The mean number of points earned is
therefore equal to 240 over four, which is 60.

The second part of the question
asks us what the mean represents. And to answer this, we need to
think about how it was calculated. We took the total number of points
earned by all four houses and divided it by four. In other words, we shared the total
number of points equally between the four houses. The mean therefore represents the
number of points that each house would have earned if the total was the same but all
houses had earned the same number of points as each other.

So we’ve completed the problem. We’ve found that the mean number of
points earned was 60. And we’ve determined that this is
the number of points each house would have earned if they had all earned the same
number of points.