UK K12 GCSE/A-Level: Year 2 KS1 Mathematics - Statistics, Pictograms and Tally Charts

Learning objectives

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

• Create and interpret pictograms and tally charts to represent data
• Understand the concept of frequency and how it relates to pictograms and tally charts
• Use pictograms and tally charts to compare and contrast data
• Begin to understand the importance of statistics in real-life contexts

Core concepts

A pictogram is a visual representation of data using pictures or symbols. It is often used to show the frequency of something, such as the number of pets in a class. A tally chart is a table used to count the frequency of something, such as the number of times a particular event occurs.

Imagine you are a teacher, and you want to know how many students in your class have a pet. You could ask each student to draw a picture of their pet on a piece of paper, and then count the number of pictures. This would be an example of a pictogram.

Frequency

Frequency is the number of times something occurs. In the example above, the frequency of students with pets would be the number of pictures drawn.

Creating pictograms and tally charts

To create a pictogram or tally chart, you need to collect data and then represent it in a visual way.

Worked examples

Example 1: Creating a pictogram

Mrs. Smith's class has 20 students. 8 students have a dog, 6 students have a cat, and 4 students have a fish. Create a pictogram to show the frequency of each type of pet.

We can use pictures to represent each type of pet. Let's use a dog for 8 students, a cat for 6 students, and a fish for 4 students.

Dog    Cat    Fish
8     6     4

This pictogram shows that 8 students have a dog, 6 students have a cat, and 4 students have a fish.

Example 2: Creating a tally chart

A school has 100 students. 30 students like reading, 25 students like writing, and 15 students like both reading and writing. Create a tally chart to show the frequency of each activity.

We can use a tally chart to count the number of students who like each activity.

This tally chart shows that 30 students like reading, 25 students like writing, and 15 students like both reading and writing.

Common misconceptions

One common misconception is that pictograms and tally charts are only used for simple data. However, they can be used to represent complex data as well.

Another common misconception is that pictograms and tally charts are only used for counting. However, they can be used to compare and contrast data as well.

Exam tips

When creating a pictogram or tally chart, make sure to:

• Use clear and concise labels
• Use consistent symbols or pictures
• Count the frequency carefully
• Use the pictogram or tally chart to compare and contrast data

When interpreting a pictogram or tally chart, make sure to:

• Read the labels carefully
• Look for patterns or trends
• Use the pictogram or tally chart to answer questions or make comparisons

MCQs with explanations

MCQ 1: [F]

What is a pictogram? A) A table used to count the frequency of something B) A visual representation of data using pictures or symbols C) A chart used to compare and contrast data D) A graph used to show trends

Correct answer: B) A visual representation of data using pictures or symbols

Why the distractors fail: A) is a description of a tally chart, not a pictogram. C) is a description of a different type of chart. D) is a description of a graph, not a pictogram.

MCQ 2: [H]

What is the frequency of something? A) The number of times something occurs B) The number of times something does not occur C) The number of times something is repeated D) The number of times something is changed

Correct answer: A) The number of times something occurs

Why the distractors fail: B) is the opposite of frequency. C) is a related concept, but not the same as frequency. D) is not related to frequency.

MCQ 3: [F]

What is a tally chart used for? A) To count the frequency of something B) To compare and contrast data C) To show trends D) To answer questions

Correct answer: A) To count the frequency of something

Why the distractors fail: B) is a related concept, but not the primary use of a tally chart. C) is not a primary use of a tally chart. D) is not a primary use of a tally chart.

MCQ 4: [H]

What is the difference between a pictogram and a tally chart? A) A pictogram uses pictures, while a tally chart uses numbers B) A pictogram uses numbers, while a tally chart uses pictures C) A pictogram is used for simple data, while a tally chart is used for complex data D) A pictogram is used for counting, while a tally chart is used for comparing and contrasting

Correct answer: A) A pictogram uses pictures, while a tally chart uses numbers

Why the distractors fail: B) is the opposite of the correct answer. C) is not true, as both pictograms and tally charts can be used for complex data. D) is not true, as both pictograms and tally charts can be used for counting.

MCQ 5: [F]

What is the importance of statistics in real-life contexts? A) To count the number of students in a class B) To compare and contrast data C) To show trends D) To answer questions

Correct answer: B) To compare and contrast data

Why the distractors fail: A) is a simple application of statistics, but not the primary importance. C) is a related concept, but not the primary importance. D) is not the primary importance of statistics.

Short-answer questions

Question 1

Create a pictogram to show the frequency of each type of pet in Mrs. Smith's class. (10 marks)

Question 2

A school has 100 students. 30 students like reading, 25 students like writing, and 15 students like both reading and writing. Create a tally chart to show the frequency of each activity. (10 marks)

Question 3

What is the difference between a pictogram and a tally chart? (5 marks)

Question 4

What is the importance of statistics in real-life contexts? (5 marks)

Question 5

Create a pictogram to show the frequency of each type of fruit in a fruit salad. (10 marks)