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Study Guide: UK K12 GCSE/A-Level: Year 6 KS2 Mathematics - Statistics, Pie Charts and Mean
Source: https://www.fatskills.com/key-stage-2-ks2/chapter/uk-k12-gcse-a-level-year-6-ks2-mathematics-statistics-pie-charts-and-mean

UK K12 GCSE/A-Level: Year 6 KS2 Mathematics - Statistics, Pie Charts and Mean

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~7 min read

Learning Objectives

By the end of this topic, students will be able to:

  • Interpret and create pie charts to represent data
  • Calculate and understand the concept of mean (average) in the context of data sets
  • Apply the mean to compare data sets and make informed decisions
  • Identify and explain the strengths and limitations of pie charts as a data representation tool

Core Concepts

A pie chart is a circular graph that shows how different categories contribute to a whole. It is often used to display data that is divided into distinct groups or categories. The size of each slice of the pie chart represents the proportion of the total data that each category represents.

The mean, or average, is a measure of the central tendency of a data set. It is calculated by adding up all the values in the data set and then dividing by the number of values. For example, if we have the following data set: 2, 4, 6, 8, 10, the mean would be calculated as (2 + 4 + 6 + 8 + 10) / 5 = 6.

Pie charts can be used to compare data sets by creating a series of pie charts, each representing a different data set. By comparing the size of each slice in each pie chart, we can see how the different categories contribute to the whole in each data set.

Worked Examples

Example 1

A survey was conducted to find out how many children in a school preferred different colors. The results are shown in the following pie chart:

If 20 children in total participated in the survey, how many children prefer the color blue?

To solve this problem, we need to find the proportion of the pie chart that represents the color blue. Since the pie chart is divided into 5 equal slices, each slice represents 1/5 of the total data. The slice representing the color blue is 2/5 of the pie chart. To find the number of children who prefer the color blue, we multiply the total number of children by the proportion of the pie chart that represents the color blue:

20 x 2/5 = 8

Therefore, 8 children prefer the color blue.

Example 2

A school is planning a trip to the zoo. The school has 50 children, and they need to decide how many buses to hire. The following data set shows the number of children who want to go on the trip:

Group Number of Children
Year 1 10
Year 2 12
Year 3 15
Year 4 8
Year 5 5

If the school wants to hire buses that can hold a maximum of 20 children, how many buses will they need to hire?

To solve this problem, we need to calculate the mean number of children per group. We can do this by adding up the number of children in each group and dividing by the number of groups:

(10 + 12 + 15 + 8 + 5) / 5 = 50 / 5 = 10

Since the mean number of children per group is 10, and each bus can hold a maximum of 20 children, the school will need to hire 3 buses (10 x 3 = 30).

Common Misconceptions

  • Students may think that the mean is always the middle value in a data set. However, this is not always the case, especially if the data set has an even number of values.
  • Students may think that pie charts are only used to display data that is divided into distinct groups or categories. However, pie charts can also be used to display data that is not divided into distinct groups or categories.
  • Students may think that the mean is always a whole number. However, the mean can be a decimal or a fraction.

Exam Tips

  • When creating a pie chart, make sure to label each slice clearly and accurately.
  • When calculating the mean, make sure to add up all the values in the data set and then divide by the number of values.
  • When comparing data sets using pie charts, make sure to look at the size of each slice in each pie chart to see how the different categories contribute to the whole in each data set.

MCQs with Explanations

MCQ 1 [F]

What is the main purpose of a pie chart?

A) To display data that is divided into distinct groups or categories B) To display data that is not divided into distinct groups or categories C) To display data that is in a table or graph D) To display data that is in a chart or diagram

Correct answer: A) To display data that is divided into distinct groups or categories

Why the distractors fail:

  • B) Pie charts can also be used to display data that is not divided into distinct groups or categories.
  • C) Pie charts are a type of graph, but they are not the only type of graph.
  • D) Pie charts are a type of chart, but they are not the only type of chart.

MCQ 2 [H]

A data set has the following values: 2, 4, 6, 8, 10. What is the mean of this data set?

A) 4 B) 6 C) 8 D) 10

Correct answer: B) 6

Why the distractors fail:

  • A) The mean is not always the middle value in a data set.
  • C) The mean is not always a whole number.
  • D) The mean is not always the largest value in a data set.

MCQ 3 [F]

What is the meaning of the term "mean"?

A) The average value of a data set B) The highest value in a data set C) The lowest value in a data set D) The range of a data set

Correct answer: A) The average value of a data set

Why the distractors fail:

  • B) The mean is not always the highest value in a data set.
  • C) The mean is not always the lowest value in a data set.
  • D) The range is the difference between the highest and lowest values in a data set.

MCQ 4 [H]

A school has 50 children, and they need to decide how many buses to hire for a trip to the zoo. The following data set shows the number of children who want to go on the trip:

Group Number of Children
Year 1 10
Year 2 12
Year 3 15
Year 4 8
Year 5 5

If the school wants to hire buses that can hold a maximum of 20 children, how many buses will they need to hire?

A) 2 B) 3 C) 4 D) 5

Correct answer: B) 3

Why the distractors fail:

  • A) The school will need to hire more than 2 buses to accommodate all the children.
  • C) The school will need to hire more than 4 buses to accommodate all the children.
  • D) The school will need to hire more than 5 buses to accommodate all the children.

MCQ 5 [H]

A data set has the following values: 1, 3, 5, 7, 9. What is the mean of this data set?

A) 3 B) 5 C) 7 D) 9

Correct answer: B) 5

Why the distractors fail:

  • A) The mean is not always the middle value in a data set.
  • C) The mean is not always a whole number.
  • D) The mean is not always the largest value in a data set.

Short-answer questions

  1. A survey was conducted to find out how many children in a school preferred different colors. The results are shown in the following pie chart:

If 20 children in total participated in the survey, how many children prefer the color blue?

  1. A school is planning a trip to the zoo. The school has 50 children, and they need to decide how many buses to hire. The following data set shows the number of children who want to go on the trip:
Group Number of Children
Year 1 10
Year 2 12
Year 3 15
Year 4 8
Year 5 5

If the school wants to hire buses that can hold a maximum of 20 children, how many buses will they need to hire?

  1. A data set has the following values: 2, 4, 6, 8, 10. What is the mean of this data set?

  2. A data set has the following values: 1, 3, 5, 7, 9. What is the mean of this data set?

  3. A school has 50 children, and they need to decide how many buses to hire for a trip to the zoo. The following data set shows the number of children who want to go on the trip:

Group Number of Children
Year 1 10
Year 2 12
Year 3 15
Year 4 8
Year 5 5

If the school wants to hire buses that can hold a maximum of 20 children, how many buses will they need to hire?