STATISTICS • USING AVERAGES 281Using averages
Whether it’s best to use the mean, median, or mode depends on
the values in your data and the type of data involved. The range
is helpful if the mean, median, and mode are all the same.Use the mean if the values in a set of data are
fairly evenly spread. Here, you can see the
savings of five children. The mean (total savings
÷ number of children) is £66.00 ÷ 5 = £13.20The mean can be misleading if one value is
much higher or lower than the rest.For example, let’s see what happens if Leroy
saves £98.50, not £14.50. Now the mean is:
£150 ÷ 5 = £30.00, which makes it seem like the
others are saving much more than they really
are. In this case, it’s better to use the median
(middle value) of £13.25. This is much closer to
the amount that most of the children save.Using the range
The range (the spread of values) can
be useful for showing a difference
between data sets when their mean,
median, and mode are the same.Emily £11.75
Ali £12.50
Josh £13.25
Manisha £14.00
Leroy £14.50
Total £66.00Emily £11.75
Ali £12.50
Josh £13.25
Manisha £14.00
Leroy £98.50
Total £150.00Median
(middle
value) is
£13.25There are
no very
high or very
low valuesBlue cars
were seen
most oftenThe mode (most common value) can
be used with data that isn't numbers.
For example, in a survey of the colours of
cars spotted, the mode might be blue.Two football teams each scored 20 goals
in five games. The mean goals scored per
match for both teams is 4 (20 ÷ 5 = 4).The range is different. It’s 8 − 1 = 7
goals for the Reds. For the Blues,
it’s 6 − 1 = 5 goals. So, the Reds’ data
has a wider spread of values.The median (middle value) for
each team is also 4 goals. So, too,
is the mode (most common value),
since both teams scored 4 goals twice.Goals scored
Reds Blues
8
4
4
3
16
5
4
4
1Total: 20 Total: 20Avoid the mean if one
value is a lot higher or
lower than the others.280_281_Range_using_averages.indd 281 29/02/2016 18:06