Pictograms and bar charts
🎯 In this topic you will
- Record, organise, and represent data using pictograms and bar charts.
- Interpret data by identifying similarities and differences, and by asking and answering questions.
🧠 Key Words
- axes
- axis
- discrete data
- represent
Show Definitions
- axes: The two reference lines on a graph that show the horizontal and vertical directions used to plot data.
- axis: A single reference line on a graph that helps locate and measure values.
- discrete data: Data that can only take specific separate values, often counted rather than measured.
- represent: To show or display information using diagrams, charts, or symbols so it can be understood clearly.
Using Pictograms to Show Data
You can use a pictogram whenever you want to make simple data look more interesting. A pictogram is a visual way of showing information by using pictures instead of lines, and it works best when the images are clear and easy to understand.
Understanding Bar Charts
Bar charts use bars to compare different sets of data. They include two axes: one vertical axis and one horizontal axis, which help show the categories and the number of items clearly.
❓ EXERCISES
$1$.
a. How many hours of sunshine were there in total on Monday and Tuesday?
b. How many more hours of sunshine were there on Wednesday than on Tuesday?
c. Use this data to complete this pictogram.
Saturday has $7\frac{1}{2}$ hours of sunshine.
Sunday has $2$ hours of sunshine less than Saturday.
Friday has the same hours of sunshine as that of Saturday and Sunday added together.
d. Add a title and a key.
👀 Show answer
a. Monday shows $2$ hours and Tuesday shows $4$ hours, so total $= 2 + 4 = 6$ hours.
b. Wednesday shows $5$ hours and Tuesday shows $4$ hours, so difference $= 1$ hour.
c. Saturday $= 7\frac{1}{2}$ hours. Sunday $= 7\frac{1}{2} - 2 = 5\frac{1}{2}$ hours. Friday $= 7\frac{1}{2} + 5\frac{1}{2} = 13$ hours.
d. Suitable title example: Hours of Sunshine. Key example: one sun symbol represents $1$ hour.
$2$.
a. Use this data to complete the bar chart. Use a ruler. Give the bar chart a title and labels.
The pet shop has one turtle, three rabbits, six fish, eight cats and nine guinea pigs.
b. Use the data on your bar chart to write two questions for your partner to answer.
👀 Show answer
a. Bar heights: turtle $= 1$, rabbits $= 3$, fish $= 6$, cats $= 8$, guinea pigs $= 9$. Suitable title: Pets in the Pet Shop. Axes labelled with animal type and number of animals.
b. Example questions: How many more cats than rabbits? Which animal is most common?
$3$.
a. Use the spinner. Spin it $20$ times. Record the results.
b. Show the results as a bar chart or a pictogram.
c. Compare your results with a partner’s results. What is the same? What is different?
d. Why did you choose that way of representing the data?
e. Use the data on your graph to write two questions for your partner to answer.
👀 Show answer
Answers will vary depending on the $20$ spins. A correct response includes a recorded table of results, a correctly drawn bar chart or pictogram, a comparison statement, a justified choice of representation, and two valid questions based on the collected data.
$4$.
a. Ask five friends, and yourself, for the number of letters in their first name.
b. Draw a bar chart and a pictogram of your data.
c. What did you find out?
d. Write three sentences about your data.
👀 Show answer
Answers will vary depending on the names collected. A correct response includes accurate data collection, correctly drawn charts, a valid conclusion about the data, and three relevant descriptive sentences.
🧠 Think like a Mathematician
Activity: You will need two six-sided dice.
Method:
- Throw the two dice $20$ times. Record how many times you get a total of $7$.
- Use a bar chart to record your results.
- Give the bar chart a title and axes labels.
- Write four questions about the data for others to answer.
Your Questions:
Thinking Prompt: If a six-sided die is thrown again, will the results be the same? Why not?
Show Answers
- The number of times a total of $7$ appears will vary each time because dice throws are random events.
- A total of $7$ is one of the more likely outcomes, but it will not occur the same number of times in repeated trials.
- The bar chart should include a clear title and labelled axes showing totals and frequency.
- Example questions could include: Which total appeared most often? How many times did a total of $7$ occur?