Key takeaways
- The mode is the value that appears most often.
- The mode is the value itself, not the number of times it appears.
- A list can have one mode, two or more modes, or no mode at all.
- The mode also works for non-number data, like favourite colours.
In this guide
What is the mode?
Ask your class for their favourite fruit. If more people say mango than anything else, mango is the mode. With numbers it works the same way: the mode is the number that shows up the most times.
The mode is one of three common kinds of average, next to the mean and the median.
Why does the mode matter?
The mean and median tell you about the middle. The mode tells you about popularity: the most common choice. Shops, restaurants and factories care about this, because it tells them what to make or stock the most.
The mode is the only average you can use for words. You cannot add up colours, but you can count which colour is most popular.
The formula
| Symbol | What it means | Example |
|---|---|---|
| Value | Each different number in the list | 8 |
| Frequency | How many times that value appears | 4 |
| Mode | The value with the biggest frequency | 8 |
There is no calculation beyond counting. Sorting the list first makes the counting much easier, because equal values end up next to each other.
How to find the mode step by step
- 1Sort the numbers. Equal values now sit side by side.
- 2Count each value. Write down how many times each one appears.
- 3Find the highest count. This is the top frequency.
- 4Read off the value. The value (or values) with that count is the mode.
Paste your own list into the calculator below, separated by commas. If there is a tie, the steps list every mode, and the main result shows the first of them.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Saying 0 when there is no mode. No mode and a mode of 0 mean different things.
- Missing a tie. If 3 and 7 both appear three times, report both as modes.
- Counting by eye in a long list. It is easy to miss one. Sort first, or use tally marks.
Tips and tricks
| Shoe size | Tally | Frequency |
|---|---|---|
| 7 | II | 2 |
| 8 | IIII | 4 |
| 9 | II | 2 |
| 10 | I | 1 |
- Check the total. The frequencies should add up to how many values you have. Above,
2 + 4 + 2 + 1 = 9. - Describe spread too. The range calculator shows how far apart the values are.
Where you'll use it in real life
- Shops: which shoe or shirt size to reorder first.
- Restaurants: the most ordered dish of the week.
- Surveys: the most common answer to a question, like favourite sport.
- Traffic and transport: the busiest hour of the day at a station.
Quick summary
To find the mode, count how often each value appears and pick the one that appears most. A list can have one mode, several modes, or none. Use the calculator above to count the frequencies and find the mode with every step shown.
Worked example
A shoe shop sold nine pairs of shoes this morning in sizes 7, 8, 8, 9, 10, 8, 7, 9 and 8. The owner wants to know which size to reorder first.
- 01Count frequencies: 7(2), 8(4), 9(2), 10(1)
- 02Most frequent value(s): 8 (appears 4 time(s))
- 03Mode = 8
These numbers are pre-filled in the calculator above.
Frequently asked questions
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, they are all modes. In 1, 1, 2, 3, 3 the modes are 1 and 3.
What if no number repeats?
Then the data has no mode, because no value appears more often than the others.
When is the mode better than the mean?
When you care about the most common choice, like the best-selling size or favourite colour. The mean of shoe sizes might be 8.2, but nobody wears size 8.2.
