These are three ways to describe the "center" of a list of numbers. The mean is the usual average, the median is the middle value, and the mode is the value that appears most often.
Try it with your own problem ↓
The steps
- Mean: add all the values, then divide by how many there are.
- Median: put the values in order from smallest to largest. The median is the middle one. With an even count, it is the mean of the two middle ones.
- Mode: find the value that appears most. There may be one mode, several, or none.
- Range (a bonus): the largest value minus the smallest.
A worked example
Find the mean, median and mode of 3, 9, 4, 7, 7.
- Mean: 3 + 9 + 4 + 7 + 7 = 30. There are 5 values, so 30 ÷ 5 = 6.
- Median: in order, the list is 3, 4, 7, 7, 9. The middle (third) value is 7.
- Mode: 7 appears twice and the others once, so the mode is 7.
- Range: 9 − 3 = 6.
Mean = 6, median = 7, mode = 7, range = 6.
Try it with your own problem
Open the free The Dot Plot with this example already filled in. It shows every step, and you can type over it with your own numbers.
Work it out: 3, 9, 4, 7, 7Opens The Dot Plot with this example
Or try these
- 4, 8, 6, 5, 7, with no mode
- An even count: 12, 15, 11, 15, 18, 20
- What score is needed for an average of 85?
Common mistakes
- Not sorting before finding the median. The middle of the list as written is not the median.
- Dividing by the wrong count. Count the values; don't use the biggest number.
- Forgetting that an even-sized list has two middle values. Average them.
- Saying there is no mode when every value appears once. Right: "no mode" is correct then, not 0.
Questions people ask
When is the median better than the mean?
When a few extreme values would pull the mean. One billionaire in a room changes the mean income a lot, but hardly changes the median.
Can there be more than one mode?
Yes. 2, 2, 5, 5, 8 has two modes, 2 and 5.
How do I find a missing value for a target mean?
Multiply the target mean by the count to get the needed total, then subtract the total you have. For an average of 85 over 4 tests with scores 78, 92, 81: 4 × 85 = 340, and 340 − 251 = 89.
Keep learning
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