Averages: Practice Set 2
Averages: Practice Set 2 is a second practice round for 11+ averages questions, revisiting the mean, median, mode and range before moving into harder problems such as finding a missing value from a given mean and combining two data sets.
Method
- To find the mean, add up all the values in the data set and divide the total by how many values there are.
- To find the median, arrange the values in order from smallest to largest; if there is an even number of values, average the middle two.
- The mode is the value that appears most often in the data set; a data set can have more than one mode, or none at all.
- The range is found by subtracting the smallest value from the largest value, and describes how spread out the data is.
- To find a missing value when you know the mean, multiply the mean by the number of values to find the total, then subtract the sum of the known values.
- When combining two data sets, find the total for each set first (mean x number of values), add the totals together, then divide by the combined number of values.
Worked example
Five friends have heights, in cm, of 132, 138, 129, 141 and 135. A sixth friend joins them, and the mean height of all six is now 136 cm. Work out the sixth friend's height.
- Add the five known heights: 132 + 138 + 129 + 141 + 135 = 675 cm.
- Multiply the new mean by the total number of friends: 136 x 6 = 816 cm.
- Subtract the sum of the five known heights from this total: 816 - 675 = 141 cm.
- Final answer: 141 cm.
Practice questions
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Q1Find the mean of 8, 12, 15, 9 and 16.Show answer
Answer: 12
Q2Find the median of 23, 19, 31, 27 and 15.Show answer
Answer: 23
Q3Find the mode of 4, 7, 4, 9, 7, 4 and 2.Show answer
Answer: 4
Q4Find the range of 56, 41, 68, 39 and 72.Show answer
Answer: 33
Q5The mean of four numbers is 18. Three of the numbers are 14, 22 and 19. Find the fourth number.Show answer
Answer: 17 (18 x 4 = 72, 72 - 55 = 17)
Q6Six numbers have a mean of 25. A seventh number, 39, is added. Calculate the new mean.Show answer
Answer: 27 (25 x 6 = 150, 150 + 39 = 189, 189 / 7 = 27)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The ages, in years, of five cousins are 11, 14, 9, 16 and 11. Calculate the mean age, giving your answer to 1 decimal place.
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A netball team's scores in their last 4 matches are 18, 24, 21 and x. The mean score across the 4 matches is 22. (a) Calculate the total of all four scores. (b) Calculate the value of x.
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Group A has 5 pupils with a mean test score of 64. Group B has 3 pupils with a mean test score of 80. Calculate the mean test score of all 8 pupils combined.
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Free printable worksheet
Want more practice on paper? Download the averages: practice set 2 worksheet pack - 10 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 17 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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