Four measures, four meanings
Mean = total ÷ how many; median = the middle value of the ordered list; mode = most common; range = largest − smallest (a measure of spread, not an average).
Estimated mean uses midpoints
For a grouped frequency table you cannot know exact values, so use the class midpoint : estimated mean .
Drawn from real examiner reports.
Class limits instead of midpoints for Σfx
Multiplying the frequency by the lower (or upper) limit rather than the midpoint of each class.
Examiners noted this lost 2 of 4 marks on Nov 2024 Paper 1H (Q1b).
Dividing Σfx by the wrong number
Dividing the total by the number of classes (e.g. 5) or by (midpoints) instead of by (the total frequency).
Seen on Nov 2024 Papers 1H/1F (Q1/Q18): "divide their sum (=1170) by 5".
Multiplying each frequency by the class width
Treating the class width (e.g. 5) as something to multiply the frequency by when finding Σfx.
Reported on Nov 2024 Papers 1H/1F (Q1/Q18).
Reading the median as a position, not a value
From a list/table the median is the value in the middle position — not the position number itself, and it need not be one of the listed numbers.
June 2024 Paper 2H (Q1): some gave the position (5, 10, 18) instead of the value.
Averaging the means to combine groups
To combine groups you must add the totals and divide by the overall count — not add the two means and halve.
June 2024 Paper 2H (Q12): adding two means and dividing by 2 scored nothing.
Mode is the value, not its frequency
From a frequency table the mode is the data value that occurs most often — the value with the largest frequency, not the frequency itself. If size 5 has frequency 8 (the highest), the mode is 5, not 8.
Range uses the data values, not frequencies
Range = largest − smallest data value. Students subtract the smallest frequency from the largest, or use the number of classes, instead of the actual values in the list.
Order the data before median/range
Always rewrite the list in ascending order first; many median and range slips come from an unordered list.
Add a Σfx column to the table
Set out an extra column for midpoint × frequency, then total both the f column and this Σfx column. A clear Σf and Σfx makes the final division reliable and earns the method marks.
Check the mean lies within the data
An estimated mean must fall between the smallest and largest possible data values. If your answer lies outside the range of the data you have divided by the wrong number — recheck that you used Σf.
| Measure | How to find it |
|---|---|
| Mean | add all values, divide by how many: |
| Median | order the data, take the middle value (position ) |
| Mode | the value that occurs most often |
| Range | largest − smallest (a measure of spread, not an average) |
Which average measures spread, not location?
For the data set , find the mean, median, mode and range.
