UK K12 GCSE/A-Level: Year 5 KS2 Mathematics - Data, Mean and Line Graphs

Learning objectives

By the end of this topic, students will be able to: - Understand the concept of mean and its calculation using a set of data. - Create and interpret line graphs to represent data. - Use line graphs to identify trends, patterns, and relationships between data. - Calculate the mean of a set of data and use it to answer questions about the data. - Interpret line graphs to answer questions about the data.

Core concepts

A mean is a way to describe the middle value of a set of numbers. It is calculated by adding up all the numbers and then dividing by the total number of values. For example, if we have the numbers 2, 4, 6, 8, and 10, the mean is (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

A line graph is a way to represent data on a graph. It is made up of a series of points connected by lines. Each point on the graph represents a value in the data set. The x-axis represents the category or group, and the y-axis represents the value or quantity.

Worked examples

Example 1: Calculating the mean

Tom has 5 boxes of pencils. The number of pencils in each box is 15, 20, 18, 22, and 19. What is the mean number of pencils in each box?

To calculate the mean, we add up the number of pencils in each box and then divide by the total number of boxes.

15 + 20 + 18 + 22 + 19 = 94

There are 5 boxes, so we divide the total number of pencils by 5.

94 ÷ 5 = 18.8

The mean number of pencils in each box is 18.8.

Example 2: Interpreting a line graph

The line graph shows the number of books sold by a bookstore over 5 days.

Day 1: 20 books Day 2: 25 books Day 3: 30 books Day 4: 35 books Day 5: 40 books

What can we infer from the line graph?

From the line graph, we can see that the number of books sold is increasing each day. This means that the bookstore is selling more books each day.

Common misconceptions

• Many students think that the mean is the same as the median. However, the mean is calculated by adding up all the numbers and dividing by the total number of values, while the median is the middle value when the numbers are arranged in order.
• Some students think that a line graph is the same as a bar chart. However, a line graph shows the trend of the data over time, while a bar chart shows the comparison of different categories.

Exam tips

• Make sure to read the question carefully and understand what is being asked.
• Use the formula for calculating the mean: (sum of values) / (total number of values).
• When interpreting a line graph, look for trends, patterns, and relationships between the data.
• Use the x-axis and y-axis labels to understand what the graph is representing.

MCQs with explanations

MCQ 1: [F]

What is the mean of the numbers 8, 12, 15, and 18?

A) 10 B) 12 C) 14 D) 16

Correct answer: C) 14

Why the distractors fail: A) 10 is too low because it is less than the middle value of the numbers. B) 12 is too low because it is less than the average of the numbers. D) 16 is too high because it is greater than the average of the numbers.

MCQ 2: [H]

A line graph shows the number of students in a school over 5 years. What can we infer from the graph if the number of students is increasing each year?

A) The school is getting smaller. B) The school is getting larger. C) The number of students is staying the same. D) The number of students is decreasing.

Correct answer: B) The school is getting larger.

Why the distractors fail: A) The school is getting smaller is the opposite of what the graph shows. C) The number of students is staying the same is not supported by the graph. D) The number of students is decreasing is the opposite of what the graph shows.

MCQ 3: [F]

What is the mean of the numbers 5, 7, 9, and 11?

A) 6 B) 8 C) 10 D) 12

Correct answer: B) 8

Why the distractors fail: A) 6 is too low because it is less than the average of the numbers. C) 10 is too high because it is greater than the average of the numbers. D) 12 is too high because it is greater than the average of the numbers.

MCQ 4: [H]

A line graph shows the temperature in a city over 10 days. What can we infer from the graph if the temperature is increasing each day?

A) The temperature is staying the same. B) The temperature is decreasing. C) The temperature is increasing. D) The temperature is fluctuating.

Correct answer: C) The temperature is increasing.

Why the distractors fail: A) The temperature is staying the same is not supported by the graph. B) The temperature is decreasing is the opposite of what the graph shows. D) The temperature is fluctuating is not supported by the graph.

MCQ 5: [F]

What is the mean of the numbers 2, 4, 6, and 8?

A) 3 B) 5 C) 6 D) 7

Correct answer: C) 6

Why the distractors fail: A) 3 is too low because it is less than the average of the numbers. B) 5 is too low because it is less than the average of the numbers. D) 7 is too high because it is greater than the average of the numbers.

Short-answer questions

1. A set of data has a mean of 15. If the total number of values is 5, what is the sum of the values?

(Answer should be 75)

1. A line graph shows the number of students in a school over 5 years. What can we infer from the graph if the number of students is increasing each year?

(Answer should be that the school is getting larger)

1. A set of data has a mean of 20. If the total number of values is 4, what is the sum of the values?

(Answer should be 80)

1. A line graph shows the temperature in a city over 10 days. What can we infer from the graph if the temperature is increasing each day?

(Answer should be that the temperature is increasing)

1. A set of data has a mean of 10. If the total number of values is 3, what is the sum of the values?

(Answer should be 30)