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
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the mean of 4, 7, 9, 12, 18.Show answer
Answer: 10 (add to get 50, divide by 5)
Q2Find the median of 8, 3, 15, 3, 10.Show answer
Answer: 8 (order: 3, 3, 8, 10, 15; middle value is 8)
Q3Find the mode of 5, 6, 5, 8, 6, 6, 9.Show answer
Answer: 6 (it appears three times, more than any other value)
Q4Find the range of 22, 9, 31, 14, 6, 27.Show answer
Answer: 25 (31 - 6 = 25)
Q5A set of 7 numbers has a mean of 12. Find the total of all 7 numbers.Show answer
Answer: 84 (12 x 7 = 84)
Q6The mean of 6 numbers is 15. Five of the numbers are 10, 12, 14, 18, 20. Find the sixth number.Show answer
Answer: 16 (total needed = 15 x 6 = 90; 90 - 74 = 16, since 10+12+14+18+20 = 74)
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the mean median mode and range worksheet pack - 14 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 3 of GCSE Statistics Foundation Workbook 2 and chapter 7 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on mean median mode and range, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.