Mode, median and range · Usually met around P5
Choosing the mean, median or mode
An outlier: the median. Categories: the mode.
How to do it
Method
An outlier: the median. Categories: the mode
20, 22, 25, 24, 300: mean 78, median 24 is more typical
Another way
Compare mean and median
78 and 24 far apart → an outlier
In full
Each of the three averages has its use. The mean is the total of all the values ÷ how many there are: the mean of 4, 6 and 11 is (4 + 6 + 11) ÷ 3 = 7. It uses every value: good when the values are close together, or when a total is to be shared out equally. When one value is far from the rest (an outlier), it drags the mean up or down, and the median, which only looks at the middle, better describes a typical value. The mode is the most common: right for “most popular” or “most common”, and the only one for categorical data such as flavours or colours. Check: work out the mean and the median and compare; far apart means there is an outlier.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Data: 23, 30, 26, 6, 21, 27. One value is far away from the others: an outlier. What is the outlier?
Show the answer and working
Answer: 6
The others all lie from 21 to 30; only 6 is far from them: 6 is the outlier.
Example 2
Data: 92, 42, 47, 41, 44. The mean is bigger than the median.
True or false?
Show the answer and working
Answer: True
The outlier 92 pulls the mean towards it, while the median only looks at the middle.
Example 3
Data: 23, 31, 20, 74, 27. The mean is □ and the median is □.
Fill in each box
Show the answer and working
Answer: 35，27
Mean = 175 ÷ 5 = 35; sorted, the middle is 27. The outlier 74 pulls the mean up.
Practise it in the game →Mode, median and range · Free to start, unlimited questions, no download