Bar charts, dot plots, waffle diagrams and pie charts
🎯 In this topic you will
- Interpret and represent data in bar charts, dot plots, waffle diagrams, and pie charts.
- Plan and carry out investigations using categorical data and whole numbers.
- Predict the outcome of an investigation, look for patterns, and check predictions.
🧠 Key Words
- bar chart
- data
- dot plot
- pie chart
- waffle diagram
Show Definitions
- bar chart: A graph that uses rectangular bars to compare amounts in different categories.
- data: Facts, numbers, or information collected to be studied or shown in a graph or chart.
- dot plot: A simple graph that shows values by placing dots above a number line or scale.
- pie chart: A circular chart divided into slices to show how a whole is split into parts.
- waffle diagram: A grid-based chart that uses small squares to represent parts of a total.
📊 Showing Data in Different Ways
The data in this section are all whole numbers or can be put into categories. We can represent this kind of data using bar charts, pictograms, waffle diagrams and pie charts.
❓ EXERCISES
1. This dot plot shows how many marks children scored in a test.
a. How many children scored $7$ marks?
b. How many children scored more than $5$ marks?
c. How many children took the test?
d. What is the highest score that children scored on the test?
👀 Show answer
b. $5$ children
c. $10$ children
d. $10$ marks
2. Ken and Ben record how many goals they score for the school hockey team in each match they play. These dot plots show the results.
a. In how many games did Ken score $2$ goals?
b. In how many games did Ben score $2$ goals?
c. How many matches did each player play?
d. Describe the pattern in the number of goals scored in each graph.
e. Give a possible explanation for the differences in the numbers of goals Ken and Ben scored.
👀 Show answer
b. $1$ game
c. $6$ matches each
d. Ken's goals are more evenly spread, Ben has more variation.
e. Ben may be less consistent, or Ken may be more steady in performance.
3. This bar chart shows the number of roses in bloom on the rose bushes in a park.
a. Which group shows the most common numbers of roses on the bushes?
b. Which group has the least common number of roses?
c. How many bushes had the range $7$ to $9$ roses?
d. How many bushes had the range $13$ to $15$ roses?
e. How many more plants were in the range $4$ to $6$ than $1$ to $3$?
f. How many more bushes were in the range $13$ to $15$ than $10$ to $12$?
g. How many bushes were looked at in total?
👀 Show answer
b. $1$–$3$
c. $12$ bushes
d. $10$ bushes
e. $8$ more
f. $4$ more
g. $48$ bushes
4. A farmer carried out a survey to find out how many peas grew in the pea pods.
a. What was the highest number of peas found in one pod?
b. Choose a sensible group size and draw a tally chart to record the number of pods in each group.
c. Draw a bar chart to represent the information.
d. Describe what the farmer would have found out from this data.
👀 Show answer
b–d. Answers will vary depending on grouping and interpretation.
5. A group of $20$ children each chose their favourite sport. Their choices are represented in this $100$ square waffle diagram.
a. What was the most popular sport?
b. What was the least popular sport?
c. What percentage of the children chose table tennis?
d. How many children chose table tennis?
e. What percentage of the children did not choose football?
f. How many children did not choose football?
👀 Show answer
b. Cricket
c. $30\%$
d. $6$ children
e. $70\%$
f. $14$ children
6. A different group of $20$ children chose these sports.
a. Copy and complete the table.
b. Draw a $100$ square waffle diagram to show the proportion of each sport chosen by this group of children. Don’t forget to include a key.
c. If you were organising a sporting event for both groups to take part in together, which sport would you choose? Explain your choice using the data from question $4$ and $5$.
d. Read your partner’s choice and explanation for part c). Assess whether they use the data accurately to make a convincing argument.
👀 Show answer
b–d. Answers will vary.
❓ EXERCISES
7. Two groups of art students chose their favourite tool for drawing out of chalk, ink, pastel or pencil.
a. What fraction of Group A preferred to draw with:
i. ink
ii. pastel
iii. pencil?
b. What percentage of Group B preferred to draw with:
i. chalk
ii. ink
iii. pastel?
c. Use the information from the pie charts to describe a way that the preferences of the two groups are similar.
d. Use the information from the pie charts to describe a way that the preferences of the two groups are different.
👀 Show answer
a. ii. $ \frac{3}{10} $
a. iii. $ \frac{3}{10} $
b. i. $10\%$
b. ii. $20\%$
b. iii. $40\%$
c. Both groups chose chalk the least.
d. Group B had more students choosing pastel, while Group A had equal numbers choosing ink, pastel and pencil.
8. Asif asked his friends how they travelled to school. He drew this frequency table of their answers.
Draw a pie chart to represent the data in the table.
👀 Show answer
Walk: $ \frac{5}{10} = 50\% = 180^\circ $
Car: $ \frac{1}{10} = 10\% = 36^\circ $
Bus: $ \frac{3}{10} = 30\% = 108^\circ $
Cycle: $ \frac{1}{10} = 10\% = 36^\circ $
9. Choose the graph or chart that would be best to represent data for each of these investigations.
a. Investigation: Which candidate in an election had the most votes? Would you use a bar chart or a waffle diagram? Why?
b. Investigation: Did any candidates in an election receive more than $50\%$ of the vote? Would you use a dot plot or a pie chart? Why?
👀 Show answer
b. Pie chart, because it shows parts of a whole and makes it easy to see whether any candidate has more than $50\%$.
🧠 Think like a Mathematician
Question: Choose one statistical question to investigate, such as:
• Which sport is most popular in your class?
• What is the most common shoe size in your classroom right now?
• How many of each different plant is growing in the school grounds?
• If you choose $20$ people in your school, what percentage will be left-handed?
Equipment: Notebook, ruler, calculator, graph paper
Method:
- Choose one of the statistical questions or create your own similar question.
- Write a prediction explaining what you think the result will be and why.
- Collect your data and organise it into a frequency table.
- Choose two different ways to represent your data (e.g. bar chart, dot plot, waffle diagram, or pie chart).
- Draw and label your charts clearly.
- Describe any patterns or trends you observe in your data.
- Compare your results with your prediction.
Follow-up Questions:
Show Answers
- 1: The data is usually categorical (e.g. types of sport) or discrete numerical (e.g. shoe sizes).
- 2: A bar chart or pie chart is often most helpful because it clearly shows comparisons or proportions.
- 3: The prediction may or may not be correct; this is decided by comparing the collected data with the original prediction.