Page 108 - Mathematics Coursebook

10.2 The mean

10.2 The mean

You have been using two sorts of average: the mode and the median. "e third type of average you need
to know about is the mean.

To %nd the mean of a set of numbers, you add up all the values and then divide by the number
of values.

Example: To %nd the mean of %ve masses: 12 kg, 14 kg, 15 kg, 20 kg and 23 kg, %rst %nd the total

+
+

mass. "en divide by 5. "e mean is 12 14 15+20 + 23 = 84 = 16.8 kg.

5 5
For a large set of numbers, you may need to use a frequency table.
Worked example 10.2
An ordinary six-sided dice Score 1 2 3 4 5 6
was thrown 100 times. Frequency 12 19 15 11 24 19
The table shows the
frequencies for each possible score.
Work out: a the mode b the mean.

a Mode = 5 The mode is the score with the highest
frequency.
b Mean = 3.73 Total score = 1 × 12 + 2 × 19 + 3 × 15 + 4 × 11 + 5 × 24 + 6 × 19 = 373

Mean = 373 = 3.73.
100 The mean is the total ÷ 100 because
the dice was thrown 100 times.

Notice that the mean is not one of the actual values. "is is because it has been calculated to represent
all the values. You can think of it as the score that would have resulted if every throw of the dice had

given the same number. "is is very unlikely when you actually throw a dice, but in statistics anything
might happen!
) Exercise 10.2

1 Mia measured the lengths of six pieces of string. 12 cm 9 cm 14 cm 20 cm 13 cm 10 cm
a Work out the mean length.
b How many pieces are longer than the mean length?
c How many pieces are shorter than the mean length?
2 Rex recorded the numbers of people who visited his cinema on several 68 85 31 38 103
different days.
Work out the mean number of visitors per day.
3 Leo wrote down the ages of ten members of his family. 18 18 19 20 24 26 30 32 38 45
a Work out their mean age.
b Leo has written his uncle’s age as 45 instead of 55.
Work out the correct mean age.

10 Averages 107