GCSE Statistics · Higher · Chapter 4: Tables, charts and diagrams

Two-way tables, pie charts, stem-and-leaf and misleading diagrams

About 85 minutesCalculator allowed83 marks

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Date

Do Now

The first two are what this chapter needs. The rest bring back earlier chapters so nothing is forgotten.

A1
Needed today
In a sale, all prices are reduced by $5%$ . A coat costs £ $418$ in the sale. What was its price before the sale?
[2 marks]
Answer

A2
Needed today
There are $27$ people at a concert. $\frac{1}{3}$ of them are adults and $\frac{1}{3}$ of the adults are women. How many women are at the concert?
[2 marks]
Answer
A3
From chapter 3
A basketball player scores with probability 0.6. Digits 0 to 5 mean score and 6 to 9 mean miss. Use these digits to simulate until two scores in a row: 6, 7, 9, 6, 6, 0, 3, 4, 0. How many shots does it take?
[2 marks]
Answer
A4
Maths skill
7 numbers have a mean of $23$ . 6 of the numbers are $23, 29, 25, 22, 12, 15$ . Find the other number.
[2 marks]
Answer
A5
Maths skill
A bag holds 6 red counters and some blue counters. The probability of taking a red counter is $\frac{1}{3}$ . How many blue counters are in the bag?
[2 marks]
Answer

Example, then your turn

Your teacher works through each example with you. Then try the one beside it.

Example 1

Mo wants to record the year group (Year 10 or Year 11) and the favourite sport (football, netball, tennis or other) of the students in a club. Design a two-way table he could use.

Hint One variable goes down the side, the other across the top. Add totals.

B1
A café wants to record, for each customer, the time of day (morning or afternoon) and the drink bought (tea, coffee, juice or other). Design a two-way table the café could use.
[2 marks]

Example 2

120 people at a gym were asked if they use the pool. 45% of them are men. $\frac{2}{3}$ of the men use the pool. 40 women do not use the pool. What percentage of the people who use the pool are women?

Hint Draw a two-way table: men and women down the side, pool and no pool across.

B2
A cinema sold 250 tickets for two films. 60% of the tickets were for Film A. $\frac{3}{5}$ of the Film A tickets were for adults. 70 of the Film B tickets were for children. What percentage of the children's tickets were for Film A? Give your answer to 1 decimal place.
[4 marks]
Answer

Example 3

A pie chart of the 320 members of Club P has a radius of 4 cm. Club Q has 500 members. Work out the radius of a comparative pie chart for Club Q.

Hint The AREA of the circle stands for the total, so the radius goes with the square root.

B3
A pie chart of the 180 students in Year 9 has a radius of 3 cm. Year 10 has 245 students. Work out the radius of a comparative pie chart for Year 10.
[2 marks]
Answer

Example 4

Kai drew this stem-and-leaf diagram of 12 test marks. Give two ways to improve it.

Hint What does 1 | 8 mean? Are the leaves in order?

B4
A council has the ages of the 2400 people in a village. Mo wants to show them in a stem-and-leaf diagram. Is a stem-and-leaf diagram suitable? Give a reason.
[2 marks]

Example 5

A shop sold 30 bikes in 2023 and 60 in 2024. In its chart the 2024 bar is twice as tall AND twice as wide. How many times as big does the 2024 bar look? Explain why the chart is misleading.

Hint The eye sees the area of the bar.

B5
A museum had 400 visitors in 2023 and 600 in 2024. In its chart the 2024 bar is 1.5 times as tall and 1.5 times as wide. How many times as big does the 2024 bar look? Explain why the chart is misleading.
[3 marks]

Example 6

The population pyramid shows the 36 000 people of Town M. (a) What percentage of the people are aged 60 and over? (b) How many people is that?

Hint A pyramid shows percentages of the whole town. Add the male and female bars.

B6
The population pyramid shows the 45 000 people of Town K. How many people in Town K are aged under 35?
[2 marks]
Answer

Practice

Each question asks for something different.

C1
The table shows how the students in two year groups travel to school. What percentage of the students who take the bus are in Year 11?
[2 marks]
Answer

C2
At sixth form P, 84 of the 240 students study a language. At sixth form Q, 99 of the 360 students do. Pia says, "More students study a language at Q, so languages are more popular at Q." Is Pia correct? Show your working.
[3 marks]
C3
A pie chart shows how 1080 homes are heated. The gas sector is $150°$ and the electric sector is $90°$ . How many more homes use gas than electric?
[2 marks]
Answer
C4
The composite bar chart shows the junior and senior members of three clubs. Which club has the greatest percentage of juniors? Show your working.
[2 marks]
Answer
C5
The stem-and-leaf diagram shows the times 13 patients waited at a clinic. Find the median and the range.
[2 marks]
Answer
C6
A choropleth map shades burglaries per 1000 homes in the bands 0 to 2.9, 3 to 5.9, 6 to 8.9 and 9 or more. District G had 399 burglaries in its 57 000 homes. Which band is District G in?
[2 marks]
Answer
C7
A pictogram shows the cars a garage sold in 2023 and 2024, with one car picture for every 20 cars. The pictures in the 2024 row are drawn bigger than those in the 2023 row. Explain why the pictogram is misleading.
[2 marks]
C8
Ana has the times of 25 boys and 25 girls in a race. She wants a diagram that keeps every time and compares the two groups. Which diagram should she draw? Give a reason.
[2 marks]

Exam-style questions

Answer in context, and finish with a conclusion when the question asks a question.

D1
Amir says, "The bar for people aged 80 and over is longer on Town R's population pyramid than on Town S's, so more people aged 80 and over live in Town R."
Town R has 18 000 people, and 9% of them are aged 80 and over. Town S has 42 000 people, and 5% of them are aged 80 and over. Is Amir correct? Show your working.
[3 marks]

D2
The two-way table shows the activity chosen by the 200 students in Years 12 and 13.
(a)
Work out the four missing values.
[2 marks]
Answer
(b)
One of the students who chose the gym is picked at random. Work out the probability that this student is in Year 13.
[2 marks]
Answer
(c)
Ian says, "The gym is more popular with Year 12, as more Year 12 students chose it." Use percentages to say whether Ian is correct.
[2 marks]
Total for D2: 6 marks
D3
A travel firm draws comparative pie charts of its customers' holidays. The pie chart for its 480 customers in 2023 has radius 4 cm. The pie chart for 2024 has radius 5 cm.
(a)
Work out the number of customers in 2024.
[2 marks]
Answer
(b)
The beach sector is $105°$ in 2023 and $96°$ in 2024. Jo says fewer customers chose a beach holiday in 2024. Is Jo correct? Show your working.
[3 marks]
Total for D3: 5 marks
D4
The back-to-back stem-and-leaf diagram shows the test marks of the 11 students in Class P and the 11 in Class Q. Compare the marks of the two classes. Use the median and the interquartile range.
[4 marks]
D5
The choropleth map shows the number of cases of flu in districts A to I last winter. District A has 60 000 people and District E has 18 000 people.
(a)
District A had 120 cases and District E had 90 cases. Work out the number of cases per 1000 people in each district.
[2 marks]
Answer
(b)
Kofi says people in District A were the most likely to catch flu, as A is shaded the darkest. Explain why the map does not show this, and how the map should be drawn.
[2 marks]
Total for D5: 4 marks
D6
The graph shows the price of a share in one year. Give two reasons why the graph is misleading. Use numbers from the graph.
[3 marks]
D7
The bar chart shows how the students at a school travelled to school. There were 120 students in 2023 and 150 in 2024. Lucy says that walking became more popular from 2023 to 2024. Is Lucy correct? Show your working.
[3 marks]
D8
The pie chart shows the favourite fruit of some people. 18 more people chose apples than chose pears. How many people were asked?
[3 marks]
Answer

Extension

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Comparative pie charts show the customers of Shop P and Shop Q. Shop P's has radius 6 cm and Shop Q's has radius 9 cm. Shop Q's refund sector is $40°$ and stands for 90 customers. Shop P's refund sector is $54°$ . How many of Shop P's customers asked for a refund?
[4 marks]
Hint 1 · What to try
Shop Q's $40°$ stands for 90 customers. Find Shop Q's total.
Hint 2 · The first line
The totals are in the ratio of the AREAS: $6^{2} : 9^{2}$ .
Hint 3 · The full method
Shop Q has $810$ customers, so Shop P has $810 \times \frac{36}{81} = 360$ .
Answer

E2
A club has three times as many juniors as seniors. 40% of the juniors and 70% of the seniors swim. 133 members swim. How many members are in the club?
[3 marks]
Hint 1 · What to try
Call the number of seniors $s$ . How many juniors are there?
Hint 2 · The first line
The swimmers are $0.4 \times 3 s + 0.7 s$ .
Hint 3 · The full method
$1.9 s = 133$ .
Answer
E3
A choropleth map shades cases per 1000 people. District X had 63 cases, which is 3.5 cases per 1000 people. How many more cases would put District X in the band "6 or more per 1000"?
[3 marks]
Hint 1 · What to try
Use the rate to find how many people live in District X.
Hint 2 · The first line
$63 \div 3.5 = 18$ thousand people.
Hint 3 · The full method
6 per 1000 of $18000$ people is $108$ cases.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can design, complete and read two-way tables, and compare groups of different sizes with percentages.
I can draw and read pie charts, including comparative pie charts with the right radius.
I can read stem-and-leaf diagrams, population pyramids and choropleth maps in context.
I can say exactly why a diagram misleads and how to fix it.

Answers and mark scheme

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