Averages
How to Find the Mode
To find the mode, count how many times each value appears and pick the value that appears most often. In 3, 7, 7, 2, 9, 7, 4 the mode is 7, because it shows up three times. This guide covers the step-by-step method, data sets with two modes or none, frequency tables, grouped data, and when the mode is the right average to use.
What is the mode, and how do you find it?
The mode is the most frequent value in a data set. It is one of the three classic averages, alongside the mean and the median, but it works differently: it does no arithmetic on the values at all. It only counts them. That is why the mode is the one average you can find for words, colors and categories as well as numbers.
Finding it takes three steps:
- Put the values in order (or tally them). Sorting brings equal values next to each other, so repeats are easy to see.
- Count each distinct value. Write the count beside it, or make tally marks.
- Pick the value with the highest count. If two or more values tie for the highest count, they are all modes. If every value appears the same number of times, there is no mode.
If you also need the mean, median and range of the same list, the mean, median, mode calculator finds all of them at once and shows the working for each. The rest of this page explains the method by hand, so you can check any answer and handle the awkward cases.
Worked examples: one mode, two modes, no mode
Example: one mode
Find the mode of 3, 7, 7, 2, 9, 7, 4.
The data set is unimodal: it has exactly one mode. Notice that the mode is 7 while the mean is about 5.57. The averages measure different things, so they rarely agree.
Example: two modes (bimodal)
Find the mode of 4, 8, 2, 8, 5, 4, 9.
Both values are modes. Do not average them into 6; 6 does not appear in the data at all, and the point of the mode is that it is a value that actually occurs. A data set with two modes is called bimodal.
Example: no mode
Find the mode of 3, 6, 9, 12.
When every value has the same frequency, no value stands out, so the usual convention is to say there is no mode. The same applies to 5, 5, 6, 6, 7, 7: each value appears twice, so nothing is more frequent than anything else.
0, 0, 0, 2, 5. When nothing repeats more than anything else, write “no mode,” not 0.How many modes can a data set have?
Unlike the mean and median, which always give exactly one answer, the mode can give zero, one or several. Statisticians have names for each case:
| Name | Number of modes | Example data | Mode(s) |
|---|---|---|---|
| No mode | 0 | 3, 6, 9, 12 | none |
| Unimodal | 1 | 2, 3, 4, 7, 7, 7, 9 | 7 |
| Bimodal | 2 | 2, 4, 4, 5, 8, 8, 9 | 4 and 8 |
| Trimodal | 3 | 1, 1, 2, 5, 5, 7, 9, 9 | 1, 5 and 9 |
| Multimodal | more than 1 | any data with a tie for top count | all tied values |
A bimodal result is often a clue rather than a nuisance. If the heights in a sample have two peaks, the sample may mix two groups, such as children and adults. If a store sells mostly shoe size 8 and size 10 and few size 9s, the customer base may be split between two kinds of buyer. One average would hide that; the two modes reveal it.
How to find the mode from a frequency table
When the data comes already counted in a frequency table, the counting step is done for you. The mode is the value in the row with the largest frequency. Read the frequency column, find the biggest number, and report the value beside it, not the frequency itself.
Example: shoe sizes sold in one day
| Shoe size | Pairs sold (frequency) |
|---|---|
| 6 | 3 |
| 7 | 8 |
| 8 | 14 |
| 9 | 11 |
| 10 | 6 |
| 11 | 2 |
A total of 44 pairs were sold. The mean size works out to about 8.34, which is not a size anyone can buy. The mode, size 8, is the answer a store manager can act on: it is the size to keep most of in stock.
The same table gives the median too: the 22nd and 23rd pairs in order are both size 8. The guide to finding the median shows how to locate middle positions in a frequency table.
How to find the mode of grouped data
Grouped data lists class intervals such as 20–30 instead of individual values, so you can no longer see which exact value occurs most. There are two levels of answer.
The modal class
The class with the highest frequency is the modal class. For many questions, “the modal class is 20–30” is the complete answer.
Estimating the mode inside the modal class
If you need a single number, use the grouped-data mode formula. It leans the estimate toward whichever neighboring class is bigger.
Example: minutes spent on homework
| Minutes | Students |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 12 |
| 30–40 | 7 |
| 40–50 | 3 |
The estimate sits a little below the middle of the class (25), because the class before it (8 students) is bigger than the class after it (7 students). Treat the result as an estimate: the original values are gone, so no method can recover the true mode exactly.
Mode vs mean vs median: when the mode is the right choice
All three are averages, but each answers a different question. The mean shares the total out evenly, the median finds the middle, and the mode finds the most common. The guide to the four averages covers the mean and median in depth; here is how the mode compares on one data set.
Example: seven salaries, in thousands of dollars
The single $250,000 salary drags the mean up to $75,000, higher than six of the seven people earn. The median, $45,000, describes a typical person better. The mode, $41,000, tells you only that two people happen to share a salary, which says little here. On numbers that rarely repeat exactly, the mode is weak.
Use the mode when:
- The data is categorical. Favorite color, car brand, blood type, survey answers. You cannot add “red” and “blue,” so there is no mean or median, but there is a most common answer.
- You care about the most popular option. The most-ordered pizza, the most common dress size, the most frequent complaint. A store stocks for the mode, not the mean.
- Values repeat a lot. Discrete counts like number of children per household, dice rolls or shoe sizes have meaningful modes.
Avoid relying on the mode alone for continuous measurements such as weights to the gram or times to the second, where almost no two values are identical. There, the median or the mean from an average calculator carries much more information, and the spread is better described by the range.
| Question | Mean | Median | Mode |
|---|---|---|---|
| Works for categories (colors, brands)? | No | No | Yes |
| Always exactly one answer? | Yes | Yes | No |
| Pulled by one extreme value? | Yes, strongly | Barely | No |
| Is always a value from the data? | Not usually | Not always | Yes |
| Uses every value in its calculation? | Yes | No | No |
Finding the mode of words and categories
The method is identical for non-numeric data. Tally each category and report the one with the most marks.
Example: favorite fruit in a class survey
You can also express the mode as a share of the whole: apple was picked 4 out of 10 times, which is 40%. The guide to writing X out of Y as a percentage covers that conversion, and the percentage calculator does it instantly.
A share like this is called the relative frequency. It is useful when comparing modes across groups of different sizes: “apple, 4 of 10” and “apple, 12 of 50” have the same mode but very different popularity, 40% versus 24%.
Common mistakes when finding the mode
- Reporting the count instead of the value. In the shoe-size table, 14 is how many times size 8 was sold. The mode is 8.
- Averaging two modes. If 4 and 8 tie, the modes are 4 and 8. Writing 6 invents a value that never occurred.
- Saying the mode is 0 when there is no mode. Zero is only the mode if zero is the most frequent value.
- Missing repeats in an unsorted list. In
12, 5, 9, 5, 12, 7, 12it is easy to spot the two 5s and stop. Sorting first,5, 5, 7, 9, 12, 12, 12, shows that 12 appears three times and is the mode. - Treating near-equal values as equal. 4.5 and 4.50 are the same value, but 4.5 and 4.51 are not. Decide on a rounding level before counting, and apply it to every value; rounding to decimal places explains how to do that consistently.
- Using the mode as the only summary of numeric data. It ignores how far apart the values are. Pair it with the median or mean, or check the median calculator for the middle and the quartiles.
Frequently asked questions
How do you find the mode of a set of numbers?
Sort the numbers so equal values sit together, count how many times each value appears, and choose the value with the highest count. In 2, 3, 4, 7, 7, 7, 9 the value 7 appears three times, more than any other, so the mode is 7. If two values tie for the highest count, both are modes.
What if there are two modes?
Report both. A data set where two values tie for the highest frequency is called bimodal. In 2, 4, 4, 5, 8, 8, 9 the modes are 4 and 8, each appearing twice. Do not average them into 6, because the mode must be a value that actually appears in the data.
What if no number repeats?
If every value appears exactly once, the data set has no mode. The same is true when every value appears the same number of times, as in 5, 5, 6, 6, 7, 7. Write “no mode” rather than 0, because 0 would be a real mode only if zero were the most frequent value.
What is the mode of 1, 2, 2, 3, 3, 3, 4?
The mode is 3. Counting each value gives 1 once, 2 twice, 3 three times and 4 once. Three appearances is the highest count, so 3 is the single mode. For comparison, the median of this list is also 3 and the mean is 18 ÷ 7, about 2.57.
Can the mode be a decimal or a negative number?
Yes. The mode is whatever value appears most often, so it can be a decimal, a negative number or zero. In −2, −2, 0.5, 1, 3 the mode is −2. It can never be a value that is missing from the data, which is one way the mode differs from the mean.
How do you find the mode in a frequency table?
Find the largest number in the frequency column and read off the value in that same row. If shoe size 8 has the highest frequency, 14, then the mode is size 8, not 14. For grouped data, the row with the highest frequency is the modal class, and a formula can estimate a single mode inside it.
Is the mode the same as the average?
The mode is one kind of average, but when people say “the average” they usually mean the mean: the total divided by the count. The mode is simply the most common value. For 38, 41, 41, 45, 52, 58, 250 the mean is 75 while the mode is 41, so the two can be far apart.
When should I use the mode instead of the mean or median?
Use the mode for categories, such as colors or brands, where a mean is impossible, and when the most popular option is what matters, such as which size to stock. For measurements that rarely repeat exactly, like weights or times, the median or mean is usually more informative than the mode.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/how-to-find-the-mode/