# What are mode, mean, median and range?

**Contents**

**Mode, mean, median and range explained**

**Examples of mode, mean, median and range**

**Mode, mean, medium and range maths problems**

**Mode, mean, medium and range FAQs**

## 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.

## 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**What is the mean average amount they had? Round your answer to the nearest whole pence.*

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

Here are some helpful resources that will help your child understand these concepts and practise using them!

**Mean, median, mode and range puzzles**

## 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

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