These questions ask you to find or interpret the centre of a short list by position. The main decisions are how to order the values and whether the count has one middle position or two.
Order, count, find the centre
Always arrange the data from smallest to largest before looking for the centre. Count every observation, including repeats. If the count is odd, cross off one value from each end until one remains. For example, ordering 11, 3, 7 as 3, 7, 11 leaves 7 in the middle. If the count is even, cross off matching end positions until two values remain, then add those two and divide by two. For 2, 5, 9 and 14, the middle pair is 5 and 9, so the central result is 7.
| Data pattern | Centre method |
|---|---|
| Odd number of values | Take the one value in the central ordered position. |
| Even number of values | Add the two central ordered values and divide by two. |
| Repeated values | Keep every occurrence in its own position while counting inward. |
| One very large or small value | Its size does not pull the centre through the list; its ordered position is what matters. |
This central result divides the ordered observations into a lower side and an upper side. That positional idea explains why an extreme value can strongly change a total-based average while leaving the ordered centre unchanged, and why an even-count result may fall between two recorded values.
The traps
| Tempting route | How to reject it |
|---|---|
| Take the middle entry as written | Writing order is not size order. Sort the entire list before reading any central position. |
| Keep just one middle value when the count is even | Two positions share the centre, so neither one can decide the result alone. Add them and divide by two. |
| Average the outer values | The extremes mark the ends, not the centre. Remove them and work with the central position or pair. |
| Use a total-based average or the midpoint of the range | Those calculations use totals or distances. This result is controlled by ordered position. |
| Count a repeated number only once | Each observation occupies a separate place, even when several observations have the same value. |
Try it
Four pupils scored 8, 3, 12 and 5 points. What is the median score? Enter the number of points. Give your answer as a decimal.
What is the median of the six numbers 1, 3, 5, 7, 9 and 11?
- 5
- 7
- 5.5
- 6
A data set contains the values 2, 3, 4, 5 and 100. Which statements about this data set are true? Select all that apply.
- The median is 22.8 and the mean is 4.
- The value 100 pulls the median upwards as far as it pulls the mean.
- The median is 4.
- The median is 100, the largest value.
- The mean of the same five values is 22.8.