Data Handling and Averages Depth Set 2
Data Handling and Averages Depth Set 2 continues the blended style of question found in the first set, combining reading and interpreting data from tables, bar charts and pictograms with calculating the three common averages, mean, median and mode, and the range, in multi-part questions. 11+ papers commonly present one data set and ask several linked questions about it.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the data source with care first, checking the title, the axis labels or key, and the units, since a misread scale is the most common source of error.
- To find the mode, look for the value that occurs most often; to find the range, subtract the smallest value from the largest.
- To find the median, list the values in order and take the middle one, or the mean of the middle two if there is an even number of values.
- To find the mean, add every value together and divide by how many values there are.
- If the mean and all but one value are given, multiply the mean by the number of values to find the total, then subtract the known values to find the missing one.
- Re-read the original data source once you have your answer, to check the figures you used genuinely match what is shown.
Worked example
Six children scored these marks in a spelling test: 6, 9, 6, 3, 9, 9. Find the mean, median, mode and range of the scores.
- For the mean, add all the scores: 6 + 9 + 6 + 3 + 9 + 9 = 42, then divide by 6: 42 / 6 = 7.
- For the median, order the scores: 3, 6, 6, 9, 9, 9. With six values, the median is the mean of the two middle values, 6 and 9: (6 + 9) / 2 = 7.5.
- For the mode, find the score that appears most often: 9 appears three times, more than any other score, so the mode is 9.
- For the range, subtract the smallest from the largest: 9 - 3 = 6.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the range of this data set: 14, 22, 9, 30, 17.Show answer
Answer: 21
Q2Find the median of this data set: 6, 2, 9, 4, 7.Show answer
Answer: 6
Q3Find the mode of this data set: 3, 7, 7, 2, 7, 9, 3.Show answer
Answer: 7
Q4The mean of five numbers is 12. Four of the numbers are 9, 15, 10 and 14. What is the fifth number?Show answer
Answer: 12
Q5Find the mean of this data set: 5, 15, 25, 35.Show answer
Answer: 20
Q6A bar chart shows 7 pupils scored a 'yellow' vote, 4 scored 'purple', and 9 scored 'orange'. How many pupils voted in total?Show answer
Answer: 20 pupils
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The number of runs scored by a cricket team in its last 5 matches were: 120, 95, 120, 140, 105. Find the mean, the mode and the range of the runs scored.
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A pictogram shows the number of laps swum by 4 swimmers, where each full symbol represents 4 laps: Amy has 2 symbols, Ben has 3.5 symbols, Cho has 1.5 symbols, and Dan has 3 symbols. How many laps did each swimmer swim, and what is the mean number of laps across the 4 swimmers?
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The mean age of a group of 6 friends is 11 years. A seventh friend joins the group, and the new mean age of all 7 friends is 12 years. Work out the age of the seventh friend.
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Free printable worksheet
Want more practice on paper? Download the data handling and averages depth set 2 worksheet pack - 12 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 19 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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