# What are mode, mean, median and range?

We explain the meaning of the terms mode, mean, median and range, with examples of how to find each of these from a set of numbers, as well as examples of the types of questions primary-school children might be asked when interpreting data sets.

## What is mode, mean, median and range?

Until September 2015, under the old primary curriculum, children in Year 6 studied the mode, mean, median and range. The new curriculum states that they only have to learn about the mean, but they may well learn all the terms anyway.

These mathematical terms can be explained by use of the following results that show the length of time in seconds a group of children took to swim a length:

 Mark Susan Rita Rebecca Hannah Robert Matthew 9 11 9 15 12 9 10

The mode is the value that appears most often in a set of data. In this case, the mode is 9 seconds.

The mean is the total of all the values, divided by the number of values. To find the mean, we add up all the results and then divide them by the number of swimmers:

9 + 11 + 9 + 15 + 12 + 9 + 10 = 75

75 ÷ 7 = 10.71428.... which can be rounded up to 11

The median is the middle number in a list of numbers ordered from smallest to largest.

9, 9, 9, 10, 11, 12, 15

so 10 is the median of this set of results.

The range is the difference between the lowest value and the highest value, so the range here is 15 - 9 = 6.

## Mode, mean, medium and range maths problems

In Year 6, children may be given a question like the following:

I asked 12 shoppers on Monday how much money they had in loose change. Here are my results: 35p, 62p, 39p, 99p, 42p, 68p

A child would most likely be allowed a calculator to work out this question.

• They would need to add up the six amounts which would total 345p and then divide this by six, getting the answer 57.5p.
• Since the question asks you to round the answer to the nearest whole pence, the final answer would be 58p.

Children may also be asked to analyse results and give a worded answer to a problem, for example:

On Tuesday I asked another group of six shoppers and found they had between 12p and £1.30 each, with a mean value of 56p. What similarities and differences are there between the two groups?

The child would need to say that the range of results is larger, but the mean average is very similar.

## Helpful resources for mode, mean, medium and range

Finding the mode (KS2)

Mean, median, mode and range puzzles

Calculating the mean average tutorial

## Mode, mean, medium and range FAQs

How can I help my child understand these concepts better?

• Use real-life examples, like measuring the heights of family members or tracking daily temperatures.
• Practise with everyday items, such as counting the number of each type of fruit in a basket to find the mode.
• Create simple exercises, like calculating the average score from their test results.
• Use visual aids, like number lines or bar graphs, to illustrate how these concepts work.

What are common misconceptions children have about these concepts?

• Confusing the mode with the mean or median because they all deal with central values.
• Thinking that the mean always represents the typical value, even in the presence of outliers.
• Misunderstanding that the range only considers the extremes and does not provide information about the values in between.
• Believing that if there are no repeated numbers, there is no mode, whereas the mode can sometimes be identified as non-existent in such cases.

How do these concepts apply in real life?

• Mode: Used in market research to find the most popular products.
• Mean: Important in fields like economics, where average incomes or prices are analysed.
• Median: Often used in real estate to determine the middle price of homes, providing a better sense of the typical price than the mean.
• Range: Used in quality control to understand the variability in product manufacturing.

Understanding these concepts is crucial for data interpretation in various professional fields and everyday decision-making.

Can you provide a simple example to illustrate each concept?

Consider the following data set representing the number of books read by five students in a month: 3, 7, 7, 2, 5.

• Mode: 7 (since it appears most frequently)
• Mean: (3 + 7 + 7 + 2 + 5) / 5 = 24 / 5 = 4.8
• Median: Arranging the numbers in order: 2, 3, 5, 7, 7. The median is 5 (the middle value).
• Range: 7 (highest value) - 2 (lowest value) = 5