Averages

Aim: To calculate averages and the range.

The average value is a number that is typical for a set of figures.

The average is like the middle point of the numbers.

Finding the average helps you do calculations and also makes it possible

to compare sets of numbers.

What is an average??

Think…Why would we want to find an

average?

ModeThe mode is the value in the data that occurs the most.For example in a list of peoples' favourite films the mode would be the most popular choice - the one with most votes.

Example Find the mode of 6, 4, 6, 5, 3, 7, 6

You can see that 6 is the most common number in the list. There are three of them.We say that 6 is the mode of this set of data.

MedianThe median is the middle value when the data is arranged in size order.

Example Find the median of these numbers

      6, 4, 6, 5, 3    First put the numbers in order. This makes it easier to

find the median  3, 4, 5, 6, 6,

You can now see that 5 is the middle number. It is half way along the list.So the median value of this set of data is 5.

MeanThe mean average shows us what would happen if there were equal shares. (everybody got the same!)To calculate the mean:

mean value  =  total amount  ÷   number of figuresExample    

Calculate the mean of 16, 13, 21 and 14.

The total of these numbers is 16 + 13 + 21 + 14 = 64 There are 4 figures, so divide the total by 4,   64 ÷ 4 = 16     So the mean is 16

RangeThe range is a measure of spread. It describes how the data is spread out.To find the range we do:

Biggest number – Smallest numberExample

What is the range of2 5 9 6 5 10 2 11Biggest number = 10Smallest number = 2

Range = 10 – 2 = 8

From the following sets of data find the: (a)Mean(b) Mode (c) Median (d) Range

10 8 3 4 9 8 7

120 122 130 131 130 129 128 132 139

27 12 56 23 98 27 28 27

Mean = 7 Mode = 8 Median = 8 Range = 7

Mean = 129 Mode = 130 Median = 130 Range = 19

Mean = 37.25 Mode = 27 Median = 27 Range = 86

Averages from a frequency table

Aim: To be able to find the four types of average from a

frequency table

Shoe size Frequency3 34 55 106 97 88 4

Here is a frequency table:

Frequency is the number of times something occurs

Can you remember what the MODE means?The MODE is the most popular number!To find the MODE from a frequency table, it is the number with the highest frequency!

Shoe size Frequency3 34 55 106 97 88 4

Can you see the mode from your frequency table?

Look for the biggest number

10 is the highest frequency, so shoe size

5 is the mode

Can you remember what the Range is?The Range is the biggest number – the smallest numberTo find the range in a frequency table, you subtract the biggest piece of data from the smallest

Can you see the range from your frequency table?

Shoe size Frequency3 34 55 106 97 88 4

Look for the biggest and

smallest

The biggest shoe size is 8, the smallest shoe size is 3. Range is 8 – 3 = 5

Can you remember what the mean is?mean value  =  total amount  ÷   number of figuresTo find the mean from a frequency table to need to follow the steps below:Shoe size Frequency Shoe size x

frequency3 34 55 106 97 88 4

Mean = (total of shoe size x frequency) ÷ (Total frequency)

Add an extra column

3 x 3 = 94 x 5 = 205 x 10 = 506 x 9 = 547 x 8 = 568 x 4 = 32

Add an extra row to show

the total of that column

22139

Mean = 221 ÷ 39

=5.7

Can you remember what the median is?The median is the middle value when the data is put in order!To find the median of data in a frequency table, to find where the middle of the frequency will be!

Shoe size Frequency3 34 55 106 97 88 4

Find the total of the

frequency column

39

To find the median, you need to add one to the total of the frequency and divide by two

202139

So the median would be the 20th value in the tableMedian = size 6

Find the mean, mode median and range of the following tables

Shoe Size Frequency

4 3

5 4

6 5

7 2

Height (cm)

Frequency

156 21157 34158 42159 37160 19

Weight (kg)

Frequency

42 143 244 545 546 447 3