Averages
Averages are single numbers that summarise a whole data set: the mean shares the total equally between all the values, the median is the middle value once the data is ordered, and the mode is the most frequently occurring value. The range measures how spread out the data is, found by subtracting the smallest value from the largest. In 11+ maths papers these are tested using number lists and frequency tables.
Before you start
Make sure you're comfortable with these topics first:
Method
- Write out the data values, and put them in order from smallest to largest if you need the median.
- To find the mode, look for the value that appears most often; a data set can have no mode, one mode, or more than one.
- To find the median, pick the middle value; if there are two middle values (an even number of items), add them together and divide by 2.
- To find the mean, add up every value, then divide the total by how many values there are.
- To find the range, subtract the smallest value from the largest value.
- For frequency tables, multiply each value by its frequency, add these totals together, then divide by the total frequency to find the mean.
Worked example
Five numbers have a mean of 11. Four of the numbers are 8, 13, 9 and 14. Work out the fifth number.
- The mean of 5 numbers is 11, so the total of all five numbers is 11 x 5 = 55.
- Add the four known numbers: 8 + 13 + 9 + 14 = 44.
- Subtract this total from the overall total: 55 - 44 = 11.
- Check: 8 + 13 + 9 + 14 + 11 = 55, and 55 / 5 = 11, which matches the given mean.
- The fifth number is 11.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the median of the numbers 22, 15, 9, 31, 18, 27.
Five numbers have a mean of 10. Four of the numbers are 6, 12, 8 and 15. Find the fifth number.
The table shows the number of goals scored by a hockey team in each of 10 matches. Goals scored (x): 0, 1, 2, 3. Frequency (f): 2, 3, 4, 1. (a) State the modal number of goals scored. (b) Calculate the mean number of goals scored per match.
Free printable worksheet
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