Average And Range Posters

Averages and range

AVERAGES and RANGE The average gives the centre or typical value of a set of data There are 3 types of average - MODE, MEDIAN and MEAN. You must remember all three

MODE (or modal value) = Most common value The mode is the value which occurs the most. There may be more than one mode or no mode at all.

4,7,2,2,4,3 Mode = 2 and 4

6,5,1,5 Mode = 5

No value is more popular than any other

3,9,7,9,3,7 No mode MEDIAN

= Middle value once the data is sorted in order of size

If two numbers are left in the middle then the median will be half way between them.

3,7,2,5,2 = 2,2,3,5,7 Median = 3 5,8,6,9,3,1 = 1,3,5,6,8,9 Median = 5.5

20 + 36 = 56 56/2 = 28

14,20,36,40,11,53 = 11,14,20,36,40,53 Median = 28 MEAN has to be calculated: Mean is found by adding all the data then dividing by the number of numbers The mean can be affected by extreme values

7,6,2,9 Mean =

24

4

=6

8,12,15,85 Mean = © www.teachitmaths.co.uk 2016

120 4

1,0,1,5,3 Mean = = 30

10

5

=2

85 is an extreme value. It has pulled the mean upwards 26894

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Averages and range

AVERAGES and RANGE The RANGE is used to help compare different sets of data. It is usually used along with one of the averages.

RANGE = Largest – smallest

The difference between the largest and smallest

The range is a measure of spread. It shows how spread out the data is.

4,7,8,3,5,4,5,1 Range = 8 – 1 = 7 3,3,5,7,3,4,2,4 Range = 7 – 2 = 5

Data with the smallest range is said to be more consistent

Comparing Data

The team manager needs to choose between Colin and James to play in the next match. Their recent scores are shown below. Who should he select? Explain your answer. Use an average Colin: 2,0,1,1,0,5 Brian: 1,1,3,1 and the range Colin’s mean =

𝟗 𝟔

= 1.5

Brian’s mean =

𝟔 𝟒

= 1.5

Colin’s range = 5 – 0 = 5 Colin’s range = 3 – 1 = 2 Both means are the same but Colin has a smaller range so he is more consistent. Select Colin. Which average should be used We sometimes have to choose an appropriate average The MODE gives which value is likely to occur. The MEAN takes every value into account, so it can be affected by extreme high or low values. The MEDIAN tells us the middle value. Half the data is above and half is below the median. The median is not affected by extreme values. © www.teachitmaths.co.uk 2016

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