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.
Using class limits instead of midpoints for Σfx
Multiplying the frequency by the lower (or upper) limit rather than the midpoint of each class.
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).
Multiplying each frequency by the class width
Treating the class width (e.g. 5) as something to multiply the frequency by when finding Σfx.
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.
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.
Order the data before reading off median/range
Always rewrite the list in ascending order first; many median and range slips come from an unordered list.
| 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.
