Averages: Mean, Median, Mode & Range
Averages and data
An average is a single value that represents a set of numbers. In the 11+ you need the four averages and to read data from tables and charts.
The four averages
| Average | How to find it |
|---|---|
| Mean | Add all the values, then divide by how many there are |
| Median | Put the values in order, then take the middle one |
| Mode | The value that appears most often |
| Range | The biggest value minus the smallest (this shows the spread) |
Example
Data: 4, 7, 7, 2, 10
- Mean = (4 + 7 + 7 + 2 + 10) ÷ 5 = 30 ÷ 5 = 6.
- Median: in order → 2, 4, 7, 7, 10 → middle = 7.
- Mode = 7 (it appears twice).
- Range = 10 − 2 = 8.
Finding the median with an even number of values
If there are two middle numbers, the median is halfway between them (add them and divide by 2). For 3, 5, 8, 10 → middle two are 5 and 8 → median = (5 + 8) ÷ 2 = 6.5.
Working backwards from the mean
If you know the mean and how many values there are, the total = mean × number of values. This is useful for "the mean of 5 numbers is 6, four of them are… find the fifth" questions: total = 6 × 5 = 30, then subtract the four you know.
Reading charts and tables
- Bar charts: read the height of each bar against the scale.
- Pictograms: each symbol stands for a number — check the key.
- Tables: find the right row and column.
- Line graphs: read across and up to find values.
Worked example
The mean of five numbers is 8. Four of them are 6, 7, 9 and 10. Find the fifth.
- Total = mean × count = 8 × 5 = 40. Known four add to 32. Fifth = 40 − 32 = 8. ✓
Common mistakes
- Forgetting to put numbers in order before finding the median.
- Confusing mode (most common) with median (middle).
- Forgetting the range is a measure of spread, not an average.
Top tips
- Remember: mean = add and divide, median = middle, mode = most, range = biggest − smallest.
- Always order the data for the median.
- Use total = mean × number to solve "find the missing value" problems.
Quick recap
- Mean (add ÷ count), median (middle, in order), mode (most common), range (spread = max − min).
- For an even set, the median is halfway between the two middle values.
- Read data carefully from bar charts, pictograms (check the key) and tables.