The mean, the median and the mode are three different measures of average which we can use. The range is a measure of how spread out data is.

The Mode

The mode is the value that appears most often.

The Median

The median is the middle number (when the numbers are in order).

The Mean

To calculate the mean add up all the numbers and then divide by how many numbers there are.

The Range

The range is the difference between the biggest number and the smallest number.

Example 1: Here are a list of 7 numbers: 7 4 7 9 5 1 2 Find: a) The mode b) The median c) The mean d) The range

a) The mode is the most common number The only number that appears more than once is 7 The mode is 7

b) The median is the middle number (but only when the numbers are in order) We have to put the numbers in order: 1 2 4 5 7 7 9
We can now find the middle number:

The median is 5

c) To find the mean we need to add up all the numbers then divide by how many numbers there are:

1 + 2 + 4 + 5 + 7 + 7 + 9 ⁄7 = 35⁄7 = 5

The mean is 5

d) To find the range we take the smallest number away from the biggest number 9 - 1 = 8 The range is 8

Example 2: Here are a list of 8 numbers: 6 6 13 5 11 11 11 9 Find: a) The mode b) The median c) The mean d) The range

a) The mode is the most common number 11 appears three times, that is more than any other number The mode is 11

b) To find the median (the middle number) we need to put the numbers in order: 5 6 6 9 11 11 11 13

We can see that there is not one middle number, we have 9 and 11 in the middle. When this happens the median is half way between the two middle numbers, the middle of 9 and 11 is 10. We can work this out by adding 9 and 11 and then dividing by 2.

9 + 11⁄2 = 10 The median is 10

c) To find the mean we need to add up all the numbers then divide by how many numbers there are:

5 + 6 + 6 + 9 + 11 + 11 + 11 + 13⁄8 = 72⁄8 = 9

The mean is 9

d) To find the range we take the smallest number away from the biggest number 13 - 5 = 8 The range is 8

Try these:

Calculate the mode, the median, the mean and the range:

Calculate the mode, the median, the mean and the range: