GCSE Statistics · Higher · Chapter 1: Planning an investigation · Lesson 3

Grouping data and class intervals

About 55 minutesCalculator allowed43 marks

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Date

Do Now

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
For each of these, write qualitative, discrete or continuous, and give a reason. (i) the number of pages in a book (ii) the length of a phone call
[2 marks]
A2
From chapter 1
Pia writes this hypothesis: "Older trees have better trunks." Explain why it is not a suitable hypothesis, and write a better one.
[2 marks]
A3
Maths skill
$M (1, 4)$ is the midpoint of $A (6, - 5)$ and $B$ . Find the coordinates of $B$ .
[2 marks]
Answer
A4
Maths skill
Round $0.5981$ to 2 significant figures.
[2 marks]
Answer

Example, then your turn

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

Example 1

Ten leaf lengths, in cm, are
5.3, 6.0, 7.4, 8.9, 4.6, 6.2, 9.5, 8.0, 5.9, 7.1
Find the frequency of each class: $4 < l \leq 6$ , $6 < l \leq 8$ , $8 < l \leq 10$ .

Hint

6 < l \leq 8

means more than 6, up to and including 8.

B1
Ten parcel masses, in kg, are
1.8, 2.0, 3.6, 5.2, 4.0, 0.9, 2.7, 4.4, 3.1, 6.0
Find the frequency of each class: $0 < m \leq 2$ , $2 < m \leq 4$ , $4 < m \leq 6$ .
[2 marks]
Answer $\dots$ $\dots$ $\dots$

Example 2

Asha's classes for waiting times, in minutes, are 0–10, 10–20, 20–30. Explain what is wrong, and write better classes.

Hint Where does a time of exactly 10 minutes go?

B2
Rob's classes for heights, in cm, are
$150 < h < 160$ , $160 < h < 170$ , $175 < h \leq 185$ .
Give two problems with his classes.
[2 marks]

Example 3

Find the width and the midpoint of the class $15 < t \leq 25$ .

Hint Width: top minus bottom. Midpoint: halfway between.

B3
Find the width and the midpoint of the class $2.5 < m \leq 4$ .
[2 marks]
AnswerWidth $\dots\dots$ Midpoint $\dots\dots$

Example 4

A table of salaries, in £1000s, uses classes $10 < s \leq 20$ , $20 < s \leq 30$ , $30 < s \leq 60$ . Why might the last class be wider?

Hint Are there many salaries above £30 000?

B4
A gym's table of members' ages has classes $16 < a \leq 20$ , $20 < a \leq 40$ , $40 < a \leq 50$ . Lucy says, "The $20 < a \leq 40$ class has the most members, so those ages are the most common." Why might Lucy be wrong?
[2 marks]

Example 5

From the table of 32 apple masses, how many are more than 70 g? Can you say how many are more than 75 g?

Hint Which values can you see, and which are hidden inside a class?

B5
24 people give their journey time to work. How many took more than 30 minutes? Can you say how many took more than 40 minutes? Explain.
[3 marks]

Practice

C1
A value of exactly 6 is recorded. Which class does it go in: $0 < x \leq 6$ or $6 < x \leq 12$ ?
[1 mark]
Answer
C2
Write the class "more than 20 seconds, up to and including 30 seconds" using $t$ and inequality signs.
[1 mark]
Answer

C3
Write down the modal class of these leaf widths.
[1 mark]
Answer
C4
Goals scored in a season are grouped 1–5, 6–10, 11–15. Explain why the gap between 5 and 6 does not matter.
[1 mark]
C5
Puzzle times range from 12 to 58 seconds. Write five equal classes for them, starting at 10 seconds.
[2 marks]
C6
18 runners have times in $20 < x \leq 40$ minutes. Assuming the times are spread evenly, estimate how many took between 20 and 30 minutes.
[2 marks]
Answer

Exam-style questions

D1
Ola groups the ages of people at a concert as 10–20, 20–30, 30–40, 40–60. She says, "Every person fits in exactly one class."
Is Ola right? Give a reason.
[2 marks]

D2
A courier records the masses of 60 parcels.
(a)
Write down the width of the class $2 < m \leq 5$ .
[1 mark]
Answer
(b)
Assuming the masses are spread evenly in each class, estimate how many parcels are more than 2 kg and at most 3 kg.
[2 marks]
Answer
(c)
Give one reason why the courier used unequal class widths.
[1 mark]
(d)
The courier says the heaviest parcel was 10 kg. Explain why the table does not show this.
[2 marks]
Total for D2: 6 marks
D3
Josh will time 30 students solving a puzzle. He expects times between 20 and 95 seconds. His classes are:
0–20, 20–40, 40–60, more than 60.
Assess Josh's classes.
[4 marks]

Extension

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

E1
20 students record the number of books they read in a year. Sian says, "From this table the mean is 9 books." Show that Sian must be wrong.
[4 marks]
Hint 1 · What to try
Find the greatest the mean could be.
Hint 2 · The first line
Give every student the top of their class: 4, 9 or 14 books.
Hint 3 · The full method
Greatest total $6 \times 4 + 9 \times 9 + 5 \times 14 = 175$ . Divide by 20 and compare with 9.

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can sort data into inequality classes with no gaps or overlaps.
I can find widths and midpoints and explain unequal widths.
I can say what a grouped table hides.

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