Before this page: read a list of values and count how often each value appears.
The mode is the most frequent value
The mode is the value that appears most often in a list. Count each distinct value and compare the counts; the largest count identifies the mode.
The mode has the greatest frequency
- A value must appear more often than every other value to be the only mode.
- The mode is a value from the list, not a calculated total or midpoint.
Mode of 3, 5, 3, 7, 3 and 5
Count the appearances of each value.
- 3: three times; 5: twice; 7: once.3 has the greatest frequency.
- Mode = 3.The mode is the value, not the number of appearances.
The mode is 3. Unlike the mean and median, it does not need every value to be used in a calculation.
Two values can share the greatest frequency
If two values tie for the greatest frequency, both are modes. The list is then bimodal.
Modes of 2, 4, 4, 6, 8, 8 and 10
Compare the frequencies of the values.
- 4: twice; 8: twice.Both values have the largest frequency.
- Modes = 4 and 8.Neither tied value can be left out.
A list can have no mode
When every value appears once, no value has a greater frequency than the others. The list has no mode.
No repeated value
In 1, 3, 5, 7, each value appears once. There is no mode, not a mode of 1 and not a mode of 4.
The mode works for categories
Some data is made of names rather than numbers. Addition, division and ordering do not apply to categories, but counting still does.
Most common colour
The answers are red, blue, blue, green, blue and red.
- blue: three; red: two; green: one.Blue appears most often.
- Mode = blue.Blue is the only average that applies to these categories.
Common mistakes
- Choosing the largest value In 3, 5, 3, 7, 3 and 5, 7 is the largest value but appears once. The mode is 3 because it appears three times.
- Reporting the frequency instead of the value 3 appears three times, but the mode is 3, not 3 times or 3 values.
- Leaving out a tied mode In 2, 4, 4, 6, 8, 8 and 10, both 4 and 8 appear twice. The modes are 4 and 8.
Summary
- The mode is the value with the greatest frequency.
- Two values can be modes when they tie for the greatest frequency.
- A list with no repeated value has no mode.
- The mode can describe categories, where a mean or median cannot.