Mean, Median & Mode
What is the mode?
- The mode is the value that appears the most often
- The mode of 1, 2, 2, 5, 6 is 2
- There can be more than one mode
- The modes of 1, 2, 2, 5, 5, 6 are 2 and 5
- The mode can also be called the modal value
What is the median?
- The median is the middle value when you put values in size order
- The median of 4, 2, 3 can be found by
- ordering the numbers: 2, 3, 4
- and choosing the middle value, 3
- The median of 4, 2, 3 can be found by
- If you have an even number of values, find the midpoint of the middle two values
- The median of 1, 2, 3, 4 is 2.5
- 2.5 is the midpoint of 2 and 3
- The midpoint is the sum of the two middle values divided by 2
- The median of 1, 2, 3, 4 is 2.5
What is the mean?
- The mean is the sum of the values divided by the number of values
- The mean of 1, 2, 6 is (1 + 2 + 6) ÷ 3 = 3
- The mean can be fraction or a decimal
- It may need rounding
- You do not need to force it to be a whole number
- You can have a mean of 7.5 people, for example!
How do I know when to use the mode, median or mean?
- The mode, median and mean are different ways to measure an average
- In certain situations it is better to use one average over another
- For example:
- If the data has extreme values (outliers) like 1, 1, 4, 50
The mode is 1
The median is 2.5
The mean is 14- Don't use the mean (it's badly affected by extreme values)
- If the data has more than one mode
- Don't use the mode as it is not clear
- If the data is non-numerical, like dog, cat, cat, fish
- You can only use the mode
- If the data has extreme values (outliers) like 1, 1, 4, 50
Worked example
15 students were timed to see how long it took them to solve a mathematical problem. Their times, in seconds, are given below.
12 | 10 | 15 | 14 | 17 |
11 | 12 | 13 | 9 | 21 |
14 | 20 | 19 | 16 | 23 |
Find the mean time, giving your answer to 3 significant figures.
Add up all the numbers (you can add the rows if it helps)
12 + 10 + 15 + 14 + 17 = 68
11 + 12 + 13 + 9 + 21 = 66
14 + 20 + 19 + 16 + 23 = 92
Total = 68 + 66 + 92 = 226
Divide the total by the number of values (there are 15 values)
Write the mean to 3 significant figures
Remember to include the units
The mean time is 15.1 seconds (to 3 s.f.)
Write the times in order and find the middle value
The median time is 14 seconds
Explain why the median is a better measure of average time than the mode.
Try to find the mode (the number that occurs the most)
There are two modes: 12 and 14
Explain why the median is better
There is no clear mode (there are two modes, 12 and 14), so the median is better
The16th value of 95 is extreme (very high) compared to the other values
Means are affected by extreme values
The mean will be affected by the extreme value of 95 whereas the median will not