Mean, Median and Mode Explained With Simple Examples
Short answer
The mean is the sum of the values divided by how many there are. The median is the middle value when the numbers are sorted. The mode is the value that appears most often. For 2, 3, 3, 4, 5, 6, 40 the mean is 9, the median is 4 and the mode is 3. Use the median when a few extreme values would distort the mean.
“Average” sounds like a single idea, but there are several kinds, and they can give very different answers for the same data. News stories about “average income” or “average house prices” can mean different things depending on which one is used. Knowing how to calculate the mean, median and mode, and when to use each, helps you read numbers more critically and summarise your own data honestly.
The mean (arithmetic average)
Add up all the values, then divide by how many values there are.
mean = sum of values ÷ number of values
Example: 2, 3, 3, 4, 5, 6, 40. The sum is 63 and there are 7 values, so the mean is 63 ÷ 7 = 9.
Notice that 9 is bigger than six of the seven numbers. The single large value, 40, pulls the mean upwards. This is the main weakness of the mean: it is sensitive to outliers.
The median (middle value)
- Sort the values from smallest to largest.
- If there is an odd number of values, the median is the middle one.
- If there is an even number, the median is the mean of the two middle values.
Example (odd count): 2, 3, 3, 4, 5, 6, 40. The middle (4th) value is 4.
Example (even count): 2, 3, 3, 4, 5, 6. The two middle values are 3 and 4, so the median is (3 + 4) ÷ 2 = 3.5.
The median ignores how extreme the largest and smallest values are, so it is a better “typical” value for skewed data.
The mode (most common value)
The mode is the value that appears most often. In 2, 3, 3, 4, 5, 6, 40 the mode is 3. A data set can have no mode (every value appears once), one mode, or several modes (for example 1, 1, 2, 3, 3 has two modes: 1 and 3).
The mode is the only average that works for categories that are not numbers, such as the most common shoe size sold, the most popular colour or the most frequent answer in a survey.
Which average should you use?
| Average | Best for | Watch out for |
|---|---|---|
| Mean | Data without extreme values, such as test scores in a class or daily temperatures | Distorted by outliers |
| Median | Skewed data such as incomes, house prices or response times | Ignores the size of extreme values |
| Mode | Categories and the most common choice | May not exist or may not be unique |
A real-world example: salaries
A small company has seven staff with yearly salaries (in thousands) of 32, 35, 35, 38, 40, 41 and 250, where the last is the owner.
- Mean: 471 ÷ 7 ≈ 67.3 thousand.
- Median: the middle value is 38 thousand.
- Mode: 35 thousand.
A job advert claiming an “average salary of 67,000” would be technically true but misleading: six of the seven people earn far less. The median of 38,000 describes a typical employee much better. This is why official statistics on household income and house prices usually report the median.
The range: how spread out the data is
Averages tell you about the centre; the range tells you about the spread. Range = largest value − smallest value. For 2, 3, 3, 4, 5, 6, 40 the range is 40 − 2 = 38. Two classes can have the same mean score but very different ranges, so it is worth reporting both. More advanced measures of spread include the interquartile range and the standard deviation.
Weighted averages
Sometimes values matter by different amounts. A course grade might be 20% homework, 30% midterm exam and 50% final exam. If you scored 85, 78 and 92:
weighted average = 85 × 0.20 + 78 × 0.30 + 92 × 0.50 = 17 + 23.4 + 46 = 86.4
A simple mean of the three scores would be 85, which understates the importance of the strong final exam. Grade point averages work the same way, with credit hours as the weights; the GPA calculator handles that for you.
Calculate them instantly
Paste or type a list of numbers into the average calculator and it returns the mean, median, mode, range, count and sum at once. It accepts numbers separated by commas, spaces or new lines, so you can paste straight from a spreadsheet column.
Averages in spreadsheets
- Mean:
=AVERAGE(A2:A20) - Median:
=MEDIAN(A2:A20) - Mode:
=MODE(A2:A20)(orMODE.SNGL;MODE.MULTreturns several modes) - Weighted average:
=SUMPRODUCT(A2:A4, B2:B4) / SUM(B2:B4)
Common mistakes
- Forgetting to sort the numbers before finding the median.
- Using the mean for skewed data such as incomes.
- Averaging percentages or rates that have different bases; see how to calculate percentage increase for why this goes wrong, and use the percentage calculator for the individual changes.
- Treating a missing value as zero, which drags the mean down.
For more everyday number skills, read percentages in everyday life.
Frequently asked questions
How do you find the mean?
Add all the values and divide by how many values there are. For 4, 8 and 9, the mean is 21 ÷ 3 = 7.
How do you find the median with an even number of values?
Sort the values and take the mean of the two middle ones. For 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5.
Can there be more than one mode?
Yes. If two or more values tie for most frequent, the data has several modes. If every value appears once, there is no mode.
When is the median better than the mean?
When the data is skewed or has outliers, such as incomes or house prices. The median shows the typical value without being pulled by extremes.
What is a weighted average?
An average where each value is multiplied by a weight showing its importance, then divided by the sum of the weights. It is used for grades, GPAs and portfolio returns.