Three averages and one spread
An average is a single value that represents a whole set of data. In IGCSE you meet three of them.
- Mean — add all the values and divide by how many there are.
- Median — the middle value when the data is placed in order.
- Mode — the value that appears most often.
The range is not an average; it measures how spread out the data is.
Key idea
mean = (sum of values) ÷ (number of values). For a frequency table, mean = Σfx ÷ Σf. Range = largest value − smallest value.
Worked example
Worked example
Nine test scores are: 5, 7, 7, 8, 10, 12, 12, 12, 15.
Sum = 88, so mean = 88 ÷ 9 = 9.78 (3 s.f.).
Ordered already; the median is the 5th value = 10.
The mode is 12 (it occurs three times).
Range = 15 − 5 = 10.
Grouped data
With grouped data the exact values are unknown, so we use the midpoint of each class as x and calculate an estimated mean from Σfx ÷ Σf. The class with the highest frequency is the modal class.
Remember
- Always put data in order before finding the median.
- The median is less affected by an extreme value (outlier) than the mean.
- With an even number of values, the median is the mean of the middle two.