KS3 Maths · Year 7 · Chapter 16: Comparing data · Lesson 3

Comparing sets of data

Year 7About 70 minutesNo calculator46 marks

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Date

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Quick questions to start.

A1
Needed today
Work out the mean of $6$ , $9$ , $4$ and $13$ .
[1 mark]
Answer
A2
Needed today
Work out the range of $15$ , $8$ , $22$ and $11$ .
[1 mark]
Answer
A3
Last lesson
On a line graph, above what value is the point for the class $30 < t \leq 40$ plotted?
[1 mark]
Answer
A4
From chapter 15
Solve $2 (x + 5) = 3 x + 1$ .
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

These are the points two basketball players scored in five games.

Ali: $12$ , $8$ , $15$ , $10$ , $15$

Ben: $14$ , $12$ , $13$ , $15$ , $16$

Compare the two players. Use the mean and the range.

Hint The mean says who scores more on average. The range says who is more consistent: a smaller range means the scores are closer together.

B1
These are the numbers of cakes two shops sold on six days.
Shop P: $18$ , $25$ , $21$ , $30$ , $16$ , $22$
Shop Q: $24$ , $26$ , $23$ , $27$ , $25$ , $19$
Compare the two shops. Use the mean and the range.
[4 marks]

Example 2

Two pie charts show how pupils travel to two schools. At Hill School $120$ pupils were asked, and the Walk sector has an angle of $90°$ . At Lake School $60$ pupils were asked, and the Walk sector has an angle of $150°$ . Jess says, "The Walk sector is bigger for Lake School, so more pupils walk to Lake School." Is Jess right?

Hint An angle is a fraction of the circle. Find that fraction of the number of pupils asked at THAT school.

B2
Two pie charts show the favourite fruit of pupils in two year groups. In Year 7, $80$ pupils were asked and the Apple sector has an angle of $135°$ . In Year 8, $48$ pupils were asked and the Apple sector has an angle of $210°$ . Mo says, "More Year 8 pupils chose apples." Is Mo right? Show your working.
[3 marks]
Answer

Example 3

Two phones each cost £ $400$ when new. The table shows their values at the end of each year. Which phone lost more value over the four years?

Hint Compare the drop from the first value to the last value for each phone, not the values in one year.

B3
The table shows the heights of two plants, P and Q, at the end of each week. (a) Which plant grew more over the four weeks? (b) Which plant grew more in the first two weeks? Give the numbers.
[3 marks]

Practice

Year 7

C1
Two groups did the same puzzle. The table shows the mean and the range of their times. Make two comparisons between the groups.
[2 marks]
C2
In class 7R, $12$ of the $30$ pupils have a pet. In class 7S, $15$ of the $50$ pupils have a pet. Which class has the greater proportion of pupils with a pet? Show your working.
[2 marks]
Answer

C3
Ella's five test marks have a mean of $14$ . Four of the marks are $12$ , $16$ , $11$ and $17$ . (a) Work out the fifth mark. (b) Work out the range of the five marks.
[3 marks]
Answer
C4
$90$ Year 7 and $50$ Year 8 pupils chose a sport. Football is one third of the Year 7 pie chart and half of the Year 8 pie chart. How many more Year 7 pupils chose football?
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
The pie chart shows how $72$ Year 7 pupils travel to school. A quarter of the $120$ Year 8 pupils walk. Lily says, "The Walk sector is more than a quarter of the circle, so more Year 7 pupils walk."
Is Lily right? You must show your working.
[3 marks]
Answer

D2
$40$ pupils sat an English test and a History test. The bar chart shows their marks.
(a)
How many pupils scored $31$ – $40$ in English?
[1 mark]
Answer
(b)
How many more pupils scored $0$ – $10$ in History than in English?
[1 mark]
Answer
(c)
Which test did the pupils find harder? Give a reason.
[2 marks]
(d)
What fraction of the pupils scored over $20$ in English? Give your answer in its simplest form.
[2 marks]
Answer
Total for D2: 6 marks
D3
The bar chart shows how many trains were on time and how many were late at four times of day.
(a)
How many trains ran in the morning?
[1 mark]
Answer
(b)
What fraction of the trains early in the day were late? Give your answer in its simplest form.
[2 marks]
Answer
(c)
Sam says, "The morning was the worst time for late trains, because more trains were late then than at any other time." Use the chart to explain why Sam could be wrong.
[2 marks]
Total for D3: 5 marks
D4
Two teams of four runners ran a race. Team A's times, in seconds, were $52$ , $47$ , $58$ and $51$ . Team B's mean time was $1$ second less than Team A's. Three of Team B's times were $49$ , $55$ and $50$ seconds.
(a)
Work out the fourth time in Team B.
[3 marks]
Answer
(b)
Which team was more consistent? Give a reason.
[2 marks]
Total for D4: 5 marks

Extension

Stretch

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

E1
Set B is $3$ , $8$ , $12$ , $13$ . Set A is $x$ , $7$ , $11$ , $y$ , where $x$ is the smallest number in set A and $y$ is the largest. The two sets have the same mean and the same range. Work out $x$ and $y$ .
[4 marks]
Hint 1 · What to try
The mean of set B is $36 \div 4 = 9$ , so the four numbers in set A add up to $36$ .
Hint 2 · The first line
The range of set B is $13 - 3 = 10$ , so $y - x = 10$ . The mean gives $x + y + 18 = 36$ , so $x + y = 18$ .
Hint 3 · The full method
Two numbers that add to $18$ and differ by $10$ : $x = 4$ and $y = 14$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can compare two sets of data with the mean and the range.
I can compare pie charts that have different totals.
I can compare values over time from a table.
I can read comparative and composite bar charts.

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