What Is The Mean, Median, Mode And Range? Explained For Primary School Parents & Teachers

Here you can find out what mean, median, mode and range are, when they are taught in school, and how you can help children to understand them as part of their maths learning at home.

Before the 2014 curriculum reforms, pupils were expected to learn about all 4 different types of averages and solve problems based on their application. 

The national curriculum now has ‘mean’ as the only type of average that pupils need to be explicitly taught in Year 6.

Despite this, some schools continue to teach all four different averages after Year 6 have completed their end of year assessments. 

What is Mean?

To find an average of a set of data using mean you must first add up all the data points and divide the sum by the number of data points in total. 

What is Median?

The median value is the middle value after all the data points have been arranged in value order as a list of numbers.

What is Mode?

The mode is the value that appears the most number of times in a data set. 

What is Range?

The range value refers to the difference between the highest and lowest value. 

It is useful for pupils to be aware of mean, median, mode and range despite it not being an explicit requirement, as introduction at this stage proves useful for later years. When dealing with data which contains outliers, finding the mean may not always be the best option.

Year 6 Mean Worksheet - Independent Recap

This time-saving worksheet is for Year 6 statistics and includes 4 arithmetic questions, 9 consolidations questions, and 1 challenge question.

Mean, median and mode examples

To find an average, you must first have a data set. Here is the data set from a game a group of pupils were playing in the classroom.

JasonDavidYahyahJosephineChristine
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To find our 4 different averages, we need to manipulate this data using the information about how to find each particular average above.

Finding the mean?

Taking the above data as an example, to find the mean you would need to add 7, 12, 15, 7 and 4 together to get 45 and then divide this by the number of values, in this case 5. The average value is 9. With bigger numbers, pupils can use partitioning to help them with the calculations.

Because of the amount of calculating involved in finding the mean, it is referred to as the ‘meanest’ of the averages due to the amount of work pupils are required to do. This is one way in which you can remind pupils how to find the mean of a number of data points.

Finding the mode?

With our set of numbers the mode would be 7 as this appears twice in our data in the table above. Mode shares some similar orthography with the word ‘most’ which can be a useful way to get pupils to remember how to find the mode.

Finding the median?

The median is found by finding the middle value. Remember that the data needs to be placed into value order. That means we take the data values from the table and write them out in ascending order. Once that is done, our data looks like this:

4, 7, 7, 12, 15

The middle value, or median, is 7 as there are an equal number of other values either side of the second 7. When your data set contains an even number of values rather than an odd number, take the pair of numbers that would make the median, add them together and then divide them by 2.  

Finding the range?

The range is the difference between the highest and lowest values. With our data set that would be 11 as the highest value is 15 (Yahyah) and the lowest value is 4 (Christine). To find the difference you need to subtract the highest value from the lowest value.

When will my child learn all about these?

There is no requirement for median, mode and range to be taught at the primary phase of school. Mean is compulsory in Year 6 and comes under the statistics section of the national curriculum for mathematics where it states that ‘pupils should be taught to calculate and interpret the mean as an average.’ 

The non-statutory guidelines state that pupils should know when it is appropriate to find the mean of a data set.

A Y6 lesson slide teaching problem solving and finding the mean on Third Space Learning's online intervention.
A Y6 lesson slide teaching problem solving and finding the mean on Third Space Learning’s online intervention.

How does it relate to other areas of mathematics?

While there is no requirement for it to be linked to other areas of mathematics, some teachers may choose to give tasks that find the averages of particular data sets. This could include, for example, finding the mean of certain measurable characteristics of the class. For example, hand span, height or shoe size. This data could be obtained during a statistics lesson or a lesson on measurement.

The Office for National Statistics uses mean to find the mean age of the population. Any role that involves looking at statistical data will likely use all the above measures of central tendency to help draw conclusions from the data. 

People may also use the mode or modal value to estimate how long it takes them to do tasks they do frequently. 

For example, if you timed yourself hoovering where you lived and you had these times in minutes, 10, 10, 8, 13 10. You could say that it takes you around 10 minutes to hoover where you live as 10 is the value with the highest frequency in the data set.

Mean, median and mode worked example

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Use the data above to find the mean, median, mode and range of the data.

To find the mean, first add all the data sets.

To solve this we need to add 8, 12, 7, 7 5 and 15. This is 54.

Next we divide by the number of data sets. As this data is for 6 people, the number of data sets is 6. This means I need to divide 54 by 6 or know that 6 x ? = 54. This is 9. The mean is 9.

To find the median I need to re-write the data in order from least to greatest.

5, 7, 7, 8, 12, 15

I then need to find the middle value. As my data set has an even number I need to find the two middle numbers, add them and divide by 2.

My middle numbers are 7 and 8 as there are two numbers either side of them. Adding them up together gives me 15. 15 divided by 2 = 7.5.

To find the mode, I am looking for the data that appears most often. 7 is the only number that appears more than once so my mode is 7.

To find the range, you subtract the lowest value from the data set from the highest. The lowest value is 5 and the highest is 15. 15 – 5 = 10. The range is 10. 

Mean, median and mode practice question

JasonDavidYahyahJosephineSusanChristineRita
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Use the data above, and the examples from further up the page, to find the mean, median, mode and range of the data. 

Answers:

  1. Mean is 43
  2. Median is 7
  3. Mode is 4
  4. Range is 7 (11-4 = 7)

Wondering about how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try these other blogs:

You can find plenty of statistics worksheets for primary school pupils on the Third Space Learning Maths Hub

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Neil Almond
Neil Almond
Woodland AT Primary
Lead Teacher
Neil is a primary school lead teacher and TES contributor, as well as a writer for Third Space.
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Downloadable resource

Year 6 Mean Worksheet - Independent Recap

This time-saving worksheet is for Year 6 statistics and includes 4 arithmetic questions, 9 consolidations questions, and 1 challenge question.

Download Free Now!

Year 6 Mean Worksheet - Independent Recap

Downloadable resource

This time-saving worksheet is for Year 6 statistics and includes 4 arithmetic questions, 9 consolidations questions, and 1 challenge question.

Download Free Now!