# What are mode, mean, median and range?

### 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, median, 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.