Page 106 - Mathematics Coursebook

10.1 Average and range

10.1 Average and range

A statistic is a value that you calculate from a set of data.

A statistic that you will o!en see is the average.
An average is a representative value. It is a single number
that gives a general idea about a set of numbers.
You need to know about three types of average: the mode,
the median and the mean.

"ink about the ages of the people in the audience at a concert.

"e mode is the most common value. If there are more 19-year-olds
than people of any other age at the concert, then the mode, or the modal age, is 19 years.

"e median is the middle number if you put all the numbers in order. If you
lined up all the members of the audience in order of age, the age of the You will learn about the
middle person is the median. mean in the next section.
"e mean is one value that could represent the whole audience.

Another useful statistic is the di$erence between the largest and smallest numbers. "is is the range. It
shows how spread out the numbers are. If the oldest person at the concert is 75 and the youngest is 13,
the range is 62 years.

Worked example 10.1

Here are the times, in seconds, that 16 students took to run 30 39 32 35 32 37 32 37
200 metres. Work out the mode and the median. 44 30 32 38 38 41 39 32

The mode is 32 seconds. There are fi ve 32s, 32 occurs more times than any other number.
The median is 36 seconds. The numbers, in order, are:
30 30 32 32 32 32 32 35 37 37 38 38 39 39 41 44

They must be written in order, to fi nd the median.
The middle is halfway between the 8th and 9th number.
There is no middle number.

Here is an example of a large set of data recorded in a table. It shows the masses of 118 people.

"e masses are arranged in groups, called classes. " e frequency is the number of people in each class.

"e table above, called a frequency table, shows that 26 people have a mass that is in the interval from
40 to 49 kg and 39 people have a mass in the interval from 50 to 59 kg. You don’t know the actual mass

of each of the 118 people so you can’t %nd the real median or mode.
You can %nd the class that includes the greatest Mass (kg) 40–49 50–59 60–69 70–79 80–89

number of people. "is is called the modal class. Frequency 26 39 28 19 6
"e modal class for this data is 50–59 kg.

) Exercise 10.1

1 The ages, in years, of a group of students are given 11 11 12 13 13 14 15 15 15 15 15
in the box.
Work out: a the mode b the median c the range.
10 Averages 105