Finding the mean, mode, median & range are maths skills that are commonly tested in 11+ and Selective School exams in the UK.

## Examples

### Example Question 1:

12, 6, 2, 6, 11, 3, 10, 14

(a) What is the mean of these numbers?

(b) What is the median of these numbers?

(c) What is the mode of these numbers?

(d) What is the range of these numbers?

**Answers:**

(a) 8

(b) 8

(c) 6

(d) 12

**Explanations:**

(a) The mean is the average. It is found by adding all of the numbers together and then dividing that total by the number of items of data.

12 + 6 + 2 + 6 + 11 + 3 + 10 + 14 = 64, then 64 ÷ 8 = 8

(b) The median is the middle number when all the numbers are placed in size order: 2, 3, 6, 6, 10, 11, 12, 14. The middle falls between 6 and 10, which is 8.

(c) The mode is the number that occurs most often = 6.

(d) The range is the difference between the largest and smallest numbers: 14 – 2 = 12.

### Example Question 2:

Hamish, Chloe, Ethan, Hannah and Tom do a sponsored swim to raise money for their favourite charity. If the mean amount raised was … how much sponsorship did Ethan collect?

Hamish | Chloe | Ethan | Hannah | Tom |

£19.50 | £22.00 | ? | £26.00 | £32.50 |

**Answer: **£20

**Explanation:** To find the missing amount that Ethan collected in sponsorship money, you will need to do a reverse calculation. You know that the mean (average) was £24 and can calculate from that that the total amount of money was 5 × £24 = £120. Ethan’s missing value is the total amount raised (£120) minus the total given for the 4 children in the table above: £19.50 + £22 + £26.00 + £32.50 = 100.

£120 – £100 = £20

## Video Tutorials

### Mean, Median & Mode