KS3 Maths · Year 8 · Chapter 4: Using data · Lesson 3

Estimating a mean from grouped data

Year 8About 60 minutesNo calculator47 marks

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Quick questions to start.

A1
Last lesson
A two-way table shows $28$ students. $15$ are boys. $8$ of the girls have a pet. How many girls have no pet?
[1 mark]
Answer
A2
Needed today
Write down the number halfway between $15$ and $20$ .
[1 mark]
Answer
A3
Needed today
Work out the mean of $6$ , $9$ , $11$ and $14$ .
[1 mark]
Answer
A4
From chapter 3
Each exterior angle of a regular polygon is $40°$ . How many sides does it have?
[1 mark]
Answer

Example, then your turn

Year 8

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

Example 1

The table shows the masses of $20$ parcels. Work out an estimate of the mean mass.

Hint Use the mid-value of each class. Multiply it by the frequency, add up, then divide by

20

B1
The table shows the heights of $25$ seedlings. Work out an estimate of the mean height.
[3 marks]
Answer $\dots\dots$ cm

Example 2

The table shows how long $50$ customers waited at a bank. The classes are not all the same width. Work out an estimate of the mean time.

Hint The mid-value of

10 < t \leq 15

12.5

. Work out each mid-value with care.

B2
The table shows the masses of $25$ apples. Work out an estimate of the mean mass.
[3 marks]
Answer $\dots\dots$ g

Example 3

The table shows how many books $20$ students read in a term. Estimate (i) the total number of books read, (ii) the mean number of books.

Hint The class

0

–

4

holds

0, 1, 2, 3, 4

, so its mid-value is

2

B3
The table shows the number of people in each of $40$ cars. Estimate the total number of people in the cars, and the mean number of people per car to $1$ decimal place.
[3 marks]
Answertotal $\dots\dots$ mean $\dots\dots$

Example 4

The table shows the ages of $35$ people at a party. Write down (i) the modal class, (ii) the class that contains the median.

Hint The median is the

18

th age in order. Add up the frequencies from the top until you pass

18

B4
The table shows the times of $27$ runners. Write down the modal class and the class that contains the median.
[2 marks]
Answer

Practice

Year 8

C1
The table shows the scores of $40$ players in a quiz. Work out an estimate of the mean score.
[3 marks]
Answer
C2
The table shows the test marks of $30$ students. Work out the smallest possible range and the largest possible range of the marks.
[2 marks]
Answersmallest $\dots\dots$ largest $\dots\dots$

C3
Ana works out the mean of some grouped data. Explain why her answer is only an estimate, and why she uses the mid-value of each class.
[2 marks]
C4
The times of $50$ runners are grouped in a table. Every time is between $10$ and $25$ minutes. Max says his estimate of the mean time is $27.5$ minutes. Explain how you know Max is wrong.
[2 marks]

Exam-style questions

GCSE Foundation

D1
The table shows the weekly pocket money of $40$ students. Mia says, "The mid-values are $2$ , $6$ , $10$ and $14$ . $(2 + 6 + 10 + 14) \div 4 = 8$ , so an estimate of the mean is £ $8$ ."
Show that Mia is wrong. Work out an estimate of the mean.
[3 marks]
Answer $£ \dots\dots$

D2
The table shows the time $60$ students spent on homework one evening.
(a)
Write down the modal class.
[1 mark]
Answer
(b)
Write down the class that contains the median.
[1 mark]
Answer
(c)
Work out an estimate of the mean time.
[3 marks]
Answer $\dots\dots$ minutes
Total for D2: 5 marks
D3
The table shows the times of $20$ students in Year 7 and $20$ students in Year 8 to run $400$ m.
(a)
Work out an estimate of the mean time for each year group.
[4 marks]
AnswerYear 7 $\dots\dots$ s Year 8 $\dots\dots$ s
(b)
Which year group was faster? Give two reasons for your answer.
[2 marks]
Total for D3: 6 marks
D4
$30$ people did a sponsored walk. The table shows how far they walked. Each person raised £ $3$ for every kilometre they walked. Work out an estimate of the total money raised. You must show your working.
[4 marks]
Answer $£ \dots\dots$

Extension

Stretch

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

E1
The table shows how long some people waited for a train. One frequency is missing. An estimate of the mean waiting time is exactly $19$ minutes. Work out the value of $x$ .
[5 marks]
Hint 1 · What to try
Write the estimated total time and the total frequency in terms of $x$ .
Hint 2 · The first line
Total time $= 5 \times 3 + 15 x + 25 \times 9 + 35 \times 4 = 380 + 15 x$ . Total frequency $= 16 + x$ .
Hint 3 · The full method
Solve $380 + 15 x = 19 (16 + x)$ , so $380 + 15 x = 304 + 19 x$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can estimate the mean of grouped data using mid-values.
I can find the modal class and the class that contains the median.
I can use an estimated mean or total to answer a question.

Answers and mark scheme

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