Mean, median and mode are three kinds of average. The mean shares the total out equally, the median is the middle value, and the mode is the most common value.
Share out, middle, most.
2 · 4 · 4 · 7 · 8
Hello, curious mind!
What are mean, median and mode?
The mean is the total divided by how many values there are, the median is the middle value when they are in order, and the mode is the value that appears most often.
“Median” comes from the Latin medius, “middle”. “Mode” comes from the French la mode, “the fashion”: the value most in fashion.
Mean
Add them all, divide by the count.
Median
Sort them, take the middle.
Mode
The value seen most often.
Range
Largest minus smallest: the spread.
How to find the mean, median and mode
Example 1: Seven friends took a quiz marked out of 20. Their marks: 14, 9, 17, 12, 17, 11, 18.
Mean. Add: 14 + 9 + 17 + 12 + 17 + 11 + 18 = 98. Divide by 7: 14.
Median. Sort first: 9, 11, 12, 14, 17, 17, 18. The 4th value is the middle: 14.
Mode. 17 appears twice, more than any other mark: 17.
Range. 18 − 9 = 9.
The check for the mean
mean × count = total
14 × 7 = 98
Watch out!
Always sort before you find the median. In the list as given, the middle number is 12, which is wrong.
How to find the median of an even set of numbers
With an even count there are two middle values. The median is their mean.
Example 2: Six taxi trips cost AED 23, 31, 18, 27, 45 and 20.
Sort: 18, 20, 23, 27, 31, 45.
The middle pair is 23 and 27. (23 + 27) ÷ 2 = AED 25.
No fare appears twice, so this set has no mode.
A set can also have two modes: in 3, 3, 6, 9, 9 both 3 and 9 are modes.
Which average should you use?
Example 3: Five friends get weekly pocket money of AED 40, 45, 50, 55 and 410. The mean is 600 ÷ 5 = AED 120. But four of the five get AED 55 or less. The one large value, an outlier, pulls the mean up. The median, AED 50, is fairer.
Use the median
When one or two values are far from the rest, such as house prices or pay.
Use the mean
When the values are close together, so every value counts fairly.
Use the mode
When the data are not numbers, such as the most popular juice.
Add the range
Two sets can have the same mean but a very different spread.
Common mistakes with mean, median and mode
- Not sorting first. The median of 8, 1, 6 is 6, not 1.
- One middle value in an even set. For 2, 5, 7, 10 the median is 6, not 5 or 7.
- Calling the biggest number the mode. The mode is the most common value.
- Adding wrong. One slip in the total spoils the mean.
- Missing a value. Count the values before you start.
Check this with the Free BMI Maths Test
- Finds the median without sorting: CNC, concept not clear.
- Takes one middle number in an even set: CNC, concept not clear.
- Says the mode is the biggest number: CNC, concept not clear.
- Adds wrong when finding the total: CMT, calculation mistake.
- Misses a number when copying the data: CWV, copied a wrong value.
The Free BMI Maths Test finds which of the 6 mistake types your child makes, and their real maths level. About the Free BMI Maths Test
Quick check: 5 questions on averages
1. What is the median of 6, 2, 9, 4, 7?
Not quite. Sort the list first.
Yes! Sorted: 2, 4, 6, 7, 9.
Not quite. That is the mean.
2. What is the mode of 5, 8, 8, 3, 5, 8?
Yes! 8 appears three times.
Not quite. 5 appears only twice.
Not quite. 3 appears only once.
3. What is the mean of 10, 12, 15, 23?
Not quite. That is the median.
Not quite. That is the range. Add, then divide by 4.
Yes! 60 ÷ 4 = 15.
4. What is the median of 3, 5, 8, 10?
Not quite. There are two middle values. Use both.
Yes! (5 + 8) ÷ 2 = 6.5.
Not quite. Find the mean of 5 and 8.
5. Which average best describes 30, 32, 35, 31, 200?
Yes! The median is 32. The outlier 200 does not move it.
Not quite. The mean is 65.6, bigger than four of the five values.
Not quite. No value repeats, so there is no mode.
Got 2 or fewer right? Book the Free BMI Maths Test to find the cause.
Try it yourself: mean, median and mode questions
1. The mean of four numbers is 9. Three of them are 7, 8 and 12. What is the fourth?
The total is 9 × 4 = 36. Then 36 − (7 + 8 + 12) = 9.
2. Find the median and the range of 41, 38, 50, 44, 39, 47.
Sorted: 38, 39, 41, 44, 47, 50. Median = (41 + 44) ÷ 2 = 42.5. Range = 50 − 38 = 12.
3. Five values have a mean of 20. The value 30 is removed. What is the new mean?
The total was 100. Now it is 70, shared by 4 values: 17.5.
4. Can the mean, median and mode all be the same number?
Yes. In 4, 5, 5, 6 all three are 5.
What changes when you add or remove a value?
Test questions often change the data and ask what happens. Often you do not need to start again.
Remove an outlier
mean 120 → 47.5
Take AED 410 out of the pocket money set. The mean drops by 72.5, but the median only moves from 50 to 47.5.
Quick rules
new value vs mean
Add a value above the mean, and the mean goes up. Add one equal to the mean, and it stays. Add the same number to every value, and the mean, median and mode all go up by it. The range does not change.
Test prep corner
Mean, median and mode in SAT maths
College Board lists “one-variable data: distributions and measures of center and spread” as a skill in the Problem-Solving and Data Analysis area of SAT maths. These are SAT-style practice questions, not real past questions.
SAT-style: A data set has 11 different values. The largest value is increased by 55. What happens to the mean and the median?
The total goes up by 55, so the mean goes up by 55 ÷ 11 = 5. The order does not change, so the median stays the same.
SAT-style: 20 people were asked how many siblings they have. 3 said 0, 7 said 1, 6 said 2 and 4 said 3. What is the median?
The median is the mean of the 10th and 11th values in order. Values 4 to 10 are 1, and values 11 to 16 are 2. So the median is (1 + 2) ÷ 2 = 1.5.
Read our Digital SAT maths guide, or ask us about SAT maths prep on WhatsApp.
Facts checked on 6 November 2026 on satsuite.collegeboard.org.
Questions people ask about mean, median and mode
What is the difference between mean, median and mode?
The mean is the total divided by the number of values. The median is the middle value in order. The mode is the most common value.
How do I find the median of an even set of numbers?
Sort the numbers, then take the mean of the two middle values. For 4, 9, 11, 20 the median is (9 + 11) ÷ 2 = 10.
Can there be more than one mode?
Yes. If two values tie for most common, both are modes. If no value repeats, most books say there is no mode.
Which average is best when there is an outlier?
The median. An outlier pulls the mean towards it, but the median stays in the middle.
Is the median still a puzzle?
The Free BMI Maths Test finds your child’s real maths level and the reason for each mistake.
