Advanced Mean Calculations

Understanding the Mean Formula

The mean (or average) is calculated using: $\text{Mean} = \frac{\text{Total of values}}{\text{Number of values}}$

This formula can be rearranged to help solve more advanced questions: $\text{Total of values} = \text{Mean} \times \text{Number of values}$

This is especially useful when:

A value is missing from the data

A new value is added or removed

You need to work backwards to find totals or individual values

 

Example

A group of 8 friends went to a concert. The mean amount of money they each spent on tickets was £44.

(a) What was the total amount spent by the group?

Use the rearranged formula: $\text{Total} = 44 \times 8 = \pounds352$

(b) If a 9th friend joined them and the new mean was £45, how much did the 9th friend spend?

New total with 9 friends: $45 \times 9 = \pounds405$

Total spent by the original 8: $\pounds352$

Amount spent by the 9th friend: $405 - 352 = \pounds53$