11+ · Topic guide

Averages and Data Handling: Practice Set 3

Averages and Data Handling: Practice Set 3 is a practice set covering the mean, median, mode and range of a data set, and reading and interpreting data from tables, bar charts, pictograms and simple line graphs, a common numeracy skill on 11+ maths papers.

Year 5-6 (11+)Maths and Numerical ReasoningGL AssessmentCEM

Before you start

Make sure you're comfortable with these topics first:

Method

  1. When asked for the mean, add all the values together and divide by how many values there are, showing the total and the count separately.
  2. When asked for the median, put the values in order first, then find the middle value, or the mean of the two middle values if there is an even number of values.
  3. When asked for the mode, find the value that appears most often; remember a data set can have no mode, one mode, or more than one mode.
  4. When asked for the range, subtract the smallest value from the largest value.
  5. Before reading a graph or table, check the title, the axis labels, and the value each gridline or symbol represents, since one picture on a pictogram might represent several items.
  6. When comparing two data sets, use more than one measure, such as mean and range together, since a single average can hide how spread out the data is.

Worked example

Five pupils scored the following marks in a test: 14, 18, 12, 20, 16. Find the mean, median and range of these marks.

  1. Order the marks from smallest to largest: 12, 14, 16, 18, 20.
  2. Find the median: the middle value of the ordered list is 16.
  3. Find the range: 20 - 12 = 8.
  4. Find the total of all five marks: 12 + 14 + 16 + 18 + 20 = 80.
  5. Find the mean: 80 / 5 = 16.
  6. Final answer: mean 16, median 16, range 8.

Practice questions

Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.

Q1Find the mode of this data set: 3, 5, 5, 7, 8, 5, 2.Show answer

Answer: 5

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Q2Find the range of this data set: 9, 15, 4, 22, 11.Show answer

Answer: 18 (22 - 4)

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Q3Find the mean of 10, 20, 30, 40.Show answer

Answer: 25 (100 / 4)

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Q4A pictogram shows that one symbol represents 4 pupils. If a row has 3 and a half symbols, how many pupils does that represent?Show answer

Answer: 14 (3.5 x 4)

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Q5Find the median of this data set: 7, 2, 9, 4, 4.Show answer

Answer: 4 (ordered: 2, 4, 4, 7, 9, so the middle value is 4)

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Q6A bar chart shows sales of 25, 40, 15 and 20 items over four days. What was the total sold across all four days?Show answer

Answer: 100

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Exam-style questions

Written in the style of a 11+ exam paper, with a full mark scheme.

Q1[3 marks]

The number of books read by 6 pupils in a month were 3, 7, 5, 3, 8, 4. Find the mean and the mode of this data.

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Q2[5 marks]

A school recorded the number of pupils absent each day over one week: Monday 4, Tuesday 6, Wednesday 2, Thursday 9, Friday 5. Find the range of absences, the median number of absences, and state which single day's figure would change the mean the most if it were removed from the data set, giving a reason.

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Free printable worksheet

Want more practice on paper? Download the averages and data handling: practice set 3 worksheet pack - 13 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 20 of 11+ Maths Workbook 3, the whole course as one free printable PDF.

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