These questions ask which value or category occurs most often, whether several values share that status, or whether no value occurs more often than the others. You may also need to update the result after the data change.
Count frequencies, then compare the top count
Make a tally for each different value and compare the frequencies. Report the value attached to the greatest frequency, not the frequency itself. For example, in 2, 2, 2, 5, 5 and 9, the frequencies are three, two and one, so 2 is the most frequent value. The same counting method works for categories: in oak, pine, oak and birch, oak occurs most often. No adding or ordering by size is required.
| Frequency pattern | What to report |
|---|---|
| One value has the greatest count | Report that one value. |
| Some but not all distinct values tie for the greatest count | Report every value in that top tie. |
| Every value appears once | Report that there is no most frequent value. |
| A value is added or removed | Tally the changed data again; an old tie or old leader may no longer remain. |
| Zero or a non-numerical category appears | Count it normally. The result depends on frequency, not arithmetic size. |
Frequency is the count beside a value; the requested result is the value beside the greatest count. Keeping those two columns separate prevents a common label swap. When the data change, use only the observations that remain rather than carrying forward the earlier result.
The traps
| Tempting route | How to reject it |
|---|---|
| Choose the largest, central or most typical-looking value | Size and position do not determine the result. Only the frequency comparison does. |
| Keep every repeated value | Repeating is not enough when another value repeats more often. Compare all counts and keep only the highest tier. |
| Break a top tie by size or reading order | Equal highest frequencies create several correct values. Report the complete tie. |
| Reject zero as a possible result | A recorded zero is still a value, so count each occurrence normally. |
Try it
A survey records the favourite colours red, blue, blue, green and blue. What is the mode of these responses?
- Blue
- Red
- No average can be found, because colours are not numbers.
- Green
Consider the data set 2, 2, 5, 5 and 8. Which statements about the mode of this data set are true? Select all that apply.
- The value 8 is a mode.
- The value 2 is a mode.
- The data set has exactly one mode.
- The value 5 is a mode.
- The data set has no mode, because two values tie for the highest frequency.
The data set 3, 3, 5, 5 and 8 has one of its two fives removed, leaving 3, 3, 5 and 8. What is the mode of the reduced data set?
- 3
- 3 and 5 are both modes.
- 5
- There is no mode.