Mean Median Mode and Range
The mean, median and mode are three different types of average used to describe the typical value in a set of data, and the range measures how spread out the data is. The mean is the total of all the values divided by how many values there are, the median is the middle value once the data is placed in order, and the mode is the value that occurs most often. GCSE Statistics questions often ask you to calculate all four and compare them.
Before you start
No specific prerequisites - this is a good place to start.
Method
- List the data values in order from smallest to largest before finding the median, mode or range.
- For the mean, add up every value in the data set, then divide the total by the number of values.
- For the median, find the middle value in the ordered list; if there are two middle values, add them and divide by 2.
- For the mode, identify the value (or values) that appears most often; a data set can have no mode, one mode, or more than one.
- For the range, subtract the smallest value from the largest value.
- Check your answer makes sense: the mean and median should usually lie somewhere between the smallest and largest values.
Worked example
The number of goals scored by a football team in 9 matches was: 1, 3, 2, 5, 3, 2, 3, 4, 1. Find the mean, median, mode and range.
- Order the data: 1, 1, 2, 2, 3, 3, 3, 4, 5.
- Mean: add the values (1+3+2+5+3+2+3+4+1 = 24) and divide by 9, giving 24/9 = 2.67 (2 dp).
- Median: with 9 values, the middle one is the 5th value in the ordered list, which is 3.
- Mode: 3 appears three times, more than any other value, so the mode is 3.
- Range: largest value (5) minus smallest value (1) = 4.
- Final answer: mean = 2.67, median = 3, mode = 3, range = 4.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
The mean of 5 numbers is 8. Four of the numbers are 5, 9, 10, 3. Work out the fifth number.
A dice is rolled 10 times, giving the scores: 2, 5, 6, 3, 5, 1, 5, 4, 6, 3. Find the mode, the median and the range of the scores.
The mean mark for 20 students in a test was 62. It was later found that one student's mark of 45 had been recorded instead of the correct mark of 65. Work out the correct mean.
Free printable worksheet
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