Sec 1 Maths · Statistics (Sec 1)

Choosing a statistical diagram questions with answers

Practice questions on choosing a statistical diagram, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

A shop records its sales of umbrellas each month for a year and wants to show how the sales change from month to month. Which statistical diagram is the most suitable?

Step 1 of 2

What must the diagram do?

The diagram has to show how something changes over time.

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Questions

Question 1Which diagram suits the data?
A library wants an eye-catching display for children of the books borrowed each weekday with one book picture for every 10 books. Which statistical diagram is the most suitable?
Show the worked solution
1. Step 1: What must the diagram do?The diagram has to show counts with pictures and a key.
2. Step 2: So the most suitable diagram isPictogram.
Question 2Advantages and disadvantages
The diagram is an example of a pictogram. Which statement about pictograms is true?
Show the worked solution
1. Step 1: Decide whether each statement is true or falseIt is eye-catching and easy to understand at a glance. True.It does not need a key. False.Each symbol must always stand for exactly one item. False.It is the best way to show how a value changes over time. False.
2. Step 2: So the true statement isA: It is eye-catching and easy to understand at a glance.
Question 3What does the diagram tell us?
The bar graph shows the books borrowed from a school library. Which statement does the bar graph support?
Show the worked solution
1. Step 1: Check each statement against the diagram: true, false or can't tellThere are twice as many books for Wednesday as for Tuesday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . False.The number of books is smallest for Tuesday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . True.There are twice as many books for Wednesday as for Friday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . False.More books will be borrowed on Monday than on Tuesday next week. The data are only for the people and the times surveyed. Can't tell.
2. Step 2: So the statement the diagram supports isB: The number of books is smallest for Tuesday.
Question 4How many times as many?
The pictogram shows how pupils travel to school. The number of pupils for Bus is $k$ times the number for Walk. Find the value of $k$ .
Show the worked solution
1. Step 1: Count the symbols (half a symbol is 0.5)Bus: $5$ ; Walk: $2$
2. Step 2: "How many times as many" means divide $\dfrac{5}{2}$ $= 2.5$
Question 5What can NOT be justified?
The bar graph shows the bags of rice sold at a shop. Which statement can NOT be justified from the bar graph?
Show the worked solution
1. Step 1: Check each statement against the diagram: true, false or can't tellThere are 26 bags of rice altogether. Total $= 10 + 2 + 5 + 9$ $= 26$ . True.The number of bags of rice is greatest for Week 1. Week 1 $10$ ; Week 2 $2$ ; Week 3 $5$ ; Week 4 $9$ . True.There are twice as many bags of rice for Week 1 as for Week 3. Week 1 $10$ ; Week 2 $2$ ; Week 3 $5$ ; Week 4 $9$ . True.More bags of rice will be sold in Week 5 than in Week 1. The data are only for the people and the times surveyed. Can't tell.
2. Step 2: So the statement that can NOT be justified isD: More bags of rice will be sold in Week 5 than in Week 1.

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Questions

Question 1Which diagram suits the data?

A library wants an eye-catching display for children of the books borrowed each weekday with one book picture for every 10 books. Which statistical diagram is the most suitable?

Show the worked solution

Step 1: What must the diagram do?The diagram has to show counts with pictures and a key.
Step 2: So the most suitable diagram isPictogram.

Question 2Advantages and disadvantages

The diagram is an example of a pictogram. Which statement about pictograms is true?

Show the worked solution

Step 1: Decide whether each statement is true or falseIt is eye-catching and easy to understand at a glance. True.It does not need a key. False.Each symbol must always stand for exactly one item. False.It is the best way to show how a value changes over time. False.
Step 2: So the true statement isA: It is eye-catching and easy to understand at a glance.

Question 3What does the diagram tell us?

The bar graph shows the books borrowed from a school library. Which statement does the bar graph support?

Show the worked solution

Step 1: Check each statement against the diagram: true, false or can't tellThere are twice as many books for Wednesday as for Tuesday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . False.The number of books is smallest for Tuesday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . True.There are twice as many books for Wednesday as for Friday. Monday $42$ ; Tuesday $14$ ; Wednesday $34$ ; Thursday $32$ ; Friday $22$ . False.More books will be borrowed on Monday than on Tuesday next week. The data are only for the people and the times surveyed. Can't tell.
Step 2: So the statement the diagram supports isB: The number of books is smallest for Tuesday.

Question 4How many times as many?

The pictogram shows how pupils travel to school. The number of pupils for Bus is $k$ times the number for Walk. Find the value of $k$ .

Show the worked solution

Step 1: Count the symbols (half a symbol is 0.5)Bus: $5$ ; Walk: $2$
Step 2: "How many times as many" means divide $\dfrac{5}{2}$ $= 2.5$

Question 5What can NOT be justified?

The bar graph shows the bags of rice sold at a shop. Which statement can NOT be justified from the bar graph?

Show the worked solution

Step 1: Check each statement against the diagram: true, false or can't tellThere are 26 bags of rice altogether. Total $= 10 + 2 + 5 + 9$ $= 26$ . True.The number of bags of rice is greatest for Week 1. Week 1 $10$ ; Week 2 $2$ ; Week 3 $5$ ; Week 4 $9$ . True.There are twice as many bags of rice for Week 1 as for Week 3. Week 1 $10$ ; Week 2 $2$ ; Week 3 $5$ ; Week 4 $9$ . True.More bags of rice will be sold in Week 5 than in Week 1. The data are only for the people and the times surveyed. Can't tell.
Step 2: So the statement that can NOT be justified isD: More bags of rice will be sold in Week 5 than in Week 1.