Mean, Mode and Median

Learning Objective:To describe and interpret results and solutions to problems using the mode, range, mean and median.

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moderange

Do you know what these words mean?

The mode is 14 because it is the value that occurs most often. 3 children got 14, 2 children got 12 and each other score only appears once.

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The mode is the value that occurs most often in a set of results. For example, the data below shows the scores a class of children got in a spelling test:

14, 12, 14, 7, 11, 12, 17, 16, 8, 15, 14, 19, 10, 13

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The range is the difference between the smallest value and the largest value. For example, the range of the data from the spelling test is 12 because the

lowest value is 7 and the highest value is 19. The difference between 19 and 7 (19 take away 7) is 12.

14, 12, 14, 7, 11, 12, 17, 16, 11, 15, 14, 19, 10, 13

Have a look at the bar graph on the next slide. Can you work out what the mode and range are?

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A bar graph to show how many people travel in a car at once

1 2 3 4 5

2468

10121416182022

Number of people

Freq

uenc

y

What is the mode? What is the range?

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1 2 3 4 5

2

4

6

8

10

12

14

16

18

20

22

Number of people

Freq

uenc

y

The mode is 3 because 3 is the value that occurs most often. You can see this because it is the highest bar on

the bar graph.

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The range is 18 because that is the difference between the highest (22) and lowest (4) values.

1 2 3 4 5

2

4

6

8

10

12

14

16

18

20

22

Number of people

Freq

uenc

y

rang

e

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medianmean

Do you know what these words mean?

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The mean is the average value in a set of results. You can find the mean by adding all the values together and then dividing that by the number of values you added together. For example, here are the test results from 5 children’s spelling tests:

12, 15, 9, 12, 17

To find the mean, we add the scores together:

12 + 15 + 9 + 12 + 17 = 65

65 ÷ 5 = 13

We then divide the total by 5 because we added 5 values together:

This tells us that the mean (average) score was 13.

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The median is the middle value in a set of results. To find the median, you put all the values in order from lowest to highest and then find the one in the middle. For

example, here are the results from another spelling test:

11, 8, 18, 12, 17, 15, 17

8, 11, 12, 15, 17, 17, 18

First, you need to put them in order. When you have done that you can work out which value is in the middle:

If you have two middle values, you find the mean by adding the two middle numbers together and dividing them by 2:

8, 11, 12, 15, 17, 17, 18, 20

15 + 17 = 32 32 ÷ 2 = 16

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That’s a lot to remember! Let’s recap...

What is it? How do you find it?

Mean The average value Add all the values up and divide by the number of values.

Mode The value that occurs the most

See how many times each value occurs and see which one occurs most often.

Median The middle valueOrder all the values from lowest to highest and see

which is in the middle. If two are in the middle, add together and divide by 2.

Range The range of values shown

Find the difference between the lowest and highest values

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Have a look at these results from another

spelling test. What is the mode?

8

17

13

9

20

15

17

9

1117

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Did you get it right? The mode is 17 because 17 is the value that

occurs most often.

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Have a look at these results from another

spelling test. What is the range?

8

17

13

9

20

15

17

9

1117

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Did you get it right? The range is 12 because the highest value is 20

and the lowest is 8. 20-8=12

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Have a look at these results from another

spelling test. What is the mean?

8

17

13

9

20

15

17

9

1117

You might need a calculator for this one!

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Did you get it right? The mean is 13.6 because the values all

added together total 136 which you then need to divide by 10 as there

are 10 values.

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Have a look at these results from another

spelling test. What is the median?

8

17

13

9

20

15

17

9

1117

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Did you get it right? The median is 14 because the two middle values are 13 and 15.

13 + 15 = 28 28 ÷ 2 = 14