Mean, Median or Mode: Which Average Should You Use?
Mean, median and mode are all called “average” at some point, and they can give very different answers from the same data. The mean is the add-and-divide figure, the median is the middle value once the numbers are sorted, and the mode is the value that appears most often. Which one you should use depends on what you want the number to tell you.
This guide shows where they disagree and how to choose.
The three averages in plain terms
Mean
Add up all the values and divide by how many there are. Take these shoe sizes: 7, 8, 8, 8, 9, 10 and 11. The total is 61, and 61 ÷ 7 is about 8.71. The mean uses every value, which is both its strength and its weakness.
Median
Sort the values from smallest to largest and pick the middle one. The shoe sizes above are already sorted, and with seven values the fourth one is the middle, so the median is 8. When there is an even number of values, take the mean of the two middle ones. For 12, 13, 14 and 55, the middle pair is 13 and 14, so the median is 13.5.
Mode
The mode is the value that occurs most often. In the shoe-size list, 8 appears three times, so 8 is the mode. A data set can have no mode if every value is different, or more than one mode if several values tie for the top spot.
When the three disagree
Imagine five employees in a small business earning $2,000, $2,100, $2,200, $2,300 and $9,000 a month. The total is $17,600, so the mean is $3,520. The median is $2,200, the middle of the sorted list.
Neither figure is wrong; they answer different questions. The mean tells you total pay divided equally among everyone. The median tells you what a typical employee earns. Because one person earns far more than the rest, the mean sits above what four of the five people actually receive.
Which average for which job
Use the mean when the data is fairly balanced and you care about the total. Test scores, daily temperatures and weekly distances are good examples. It is also the right choice when you need to scale back up, since the mean multiplied by the count returns the original total.
Use the median when a few extreme values could distort the picture. Salaries, house prices and delivery times often work better with the median, because a single unusual entry barely moves it.
Use the mode when you are dealing with popularity or categories. A shop deciding which shoe size to stock more of cares about the most common size, not the 8.71 average.
A worked example with cashback payouts
Say your monthly cashback payments over four months were $12, $14, $13 and $55, where the last figure included a one-off promotional bonus. The mean is $94 ÷ 4 = $23.50. The median is $13.50. If you wanted to forecast a normal month, $13.50 is far more realistic than $23.50.
When a payout looks unusually high or low, it helps to check what each purchase should have earned. A cashback calculator makes that kind of check quick, so you can tell whether the odd month came from your spending or from something else.
Watch out for missing data
Averages are only as good as the data behind them. If you recorded the temperature once a day from 1 to 21 March, you should have 21 readings. Before summarising a run of daily readings, calculate days between the first and last dates, counting both ends, so you know how many values to expect. Then compare that with the number of readings you actually have and note any gaps. If you only have 19 readings, the mean describes 19 days, not 21.
Getting the mean without the arithmetic
If all you need is the mean of a long list, an average finder saves time and cuts down on arithmetic slips. For the median and mode, sorting the list is the key step, and on small data sets it is worth doing by hand so you can see the shape of your numbers.
Common mistakes to avoid
- Using the mean on skewed data. If one value is far from the rest, check the median too.
- Forgetting to sort before finding the median. The median is the middle of the sorted list, not the middle of the list as you wrote it.
- Assuming the mode is unique. Two or more values can tie, and sometimes there is no mode at all.
- Reporting “the average” without saying which one. A single sentence such as “the median salary is $2,200” removes any confusion.
A quick decision rule
Sort your data and look at it. If the numbers cluster together, the mean and median will be close, and either will do. If they pull apart, trust the median for a typical value and the mean for a total.
Final thoughts
There is no single correct average, only the right one for your question. Learn the three measures, check them against each other, and say clearly which you used. That habit alone makes your numbers far easier to trust.