Data Handling and Averages Depth
Data Handling and Averages Depth combines 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, so this set trains reading data accurately first and then applying the correct averages method to that same data.
Method
- Before calculating anything, read the data source carefully: check the title, the axis labels or key, and the units, since a misread scale is the most common cause of a wrong answer.
- To find the mode, identify the value that appears most often; to find the range, subtract the smallest value from the largest.
- To find the median, arrange the values in order from smallest to largest, then find the middle value, or the mean of the two middle values if there is an even number of values.
- To find the mean, add all the values together, then divide by how many values there are.
- When a question gives the mean and asks for a missing value, work backwards: multiply the mean by the number of values to find the total, then subtract the known values.
- Double-check by re-reading the original data source once you have an answer, to make sure the number you calculated with matches what the data actually shows.
Worked example
Five children scored these marks in a quiz: 6, 9, 7, 9, 4. Find the mean, median, mode and range of the scores.
- For the mean, add all the scores: 6 + 9 + 7 + 9 + 4 = 35, then divide by 5: 35 / 5 = 7.
- For the median, order the scores: 4, 6, 7, 9, 9. The middle value is 7.
- For the mode, find the score that appears most often: 9 appears twice, more than any other score, so the mode is 9.
- For the range, subtract the smallest from the largest: 9 - 4 = 5.
Practice questions
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Q1Find the range of this data set: 12, 18, 7, 22, 15.Show answer
Answer: 15
Q2Find the median of this data set: 3, 8, 5, 8, 2, 9, 4.Show answer
Answer: 5
Q3Find the mode of this data set: 2, 5, 5, 3, 5, 8, 2.Show answer
Answer: 5
Q4The mean of four numbers is 10. Three of the numbers are 8, 11 and 9. What is the fourth number?Show answer
Answer: 12
Q5Find the mean of this data set: 10, 20, 30, 40.Show answer
Answer: 25
Q6A bar chart shows 5 pupils scored a 'red' vote, 8 scored 'blue', and 3 scored 'green'. How many pupils voted in total?Show answer
Answer: 16 pupils
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The number of goals scored by a football team in its last 6 matches were: 2, 4, 1, 4, 3, 4. Find the mean, the mode and the range of the number of goals.
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A pictogram shows the number of books read by 4 pupils, where each full book symbol represents 4 books: Ali has 3 symbols, Bea has 2.5 symbols, Cara has 1 symbol, and Dev has 3.5 symbols. How many books did each pupil read, and what is the mean number of books read across the 4 pupils?
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Free printable worksheet
Want more practice on paper? Download the data handling and averages depth worksheet pack - 11 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 18 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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