Some grandparents took their
grandchildren to the swimming pool. The ages of the people present in
the swimming pool are shown in the grid. Simon wants to find the average age
of the people in the swimming pool. Which average is the most
appropriate? Tick the correct box. Is it the median, mean, or
mode? And give a single reason for why
each of the other two averages would not be appropriate.
Let’s recap on our understanding of
the three measures of average and their benefits. The median is the middle value when
the list is in order. The median tends to be less
affected by outliers; those are extreme values that don’t fit the pattern.
Let’s list the ages of the people
present in the swimming pool in order of size. It’s three, four, five, six, seven,
58, 61, 62, and 70. One way of finding the median — the
middle value — is to start crossing off values from the outside in. So we cross off three and 70. We cross off four and 62, five and
61, and six and 58. And we’re left with seven.
The median age then of the people
present in the swimming pool is seven. This isn’t usually representative
of the data given. We are not going to use the median
then. Because the median is only seven,
it ignores all the ages of the grandparents.
What about the mean? The mean is found by adding the
numbers together and dividing by how many we have. The mean is really useful because
it takes all data into account. And we saw that the median didn’t
really do that. We ended up with an unusually low
value, giving the ages of the grandparents. So the mean might be a good option
Let’s briefly consider the
mode. The mode is the most common
value. It is the value that occurs the
most. There is no mode for this set of
data. So that means we wouldn’t choose
that for a measure of average.
This means that we are going to
need to use the mean. And the reasons that are most
appropriate are well firstly, the median is seven, which ignores all of the ages of
the grandparents and secondly, no age occurs more frequently than the other. There’s no mode. So we can’t use it.