GCSE Maths · Higher · Chapter 18: Sampling and more complex diagrams · Lesson 4

Histograms

Grades 6–8About 50 minutesCalculator allowed33 marks

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NameClassDate

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Grades 4–6

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

A1
Needed today
Classes $0 < x \leq 10$ , $10 < x \leq 20$ , $20 < x \leq 30$ have frequencies 2, 3, 5. Work out $Σ f x$ using the midpoints.
[1 mark]
Answer
A2
Last lesson
The lower quartile is 24 and the upper quartile is 40. Find the interquartile range.
[1 mark]
Answer
A3
From chapter 4
Find the 22nd term of the sequence with $n$ th term $3 n + 3$ .
[1 mark]
Answer
A4
From chapter 5
Boys to girls is $2 : 5$ . There are 10 boys. How many girls?
[1 mark]
Answer

Grades 6–7

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

Example 1

The table shows the masses of some parcels. Work out the frequency density of each class.

Hint Frequency density is frequency divided by class width. The first class is

10

wide, so

14 \div 10 = 1.4

B1
The table shows the times some students spent on homework. Work out the frequency density of each class.
[3 marks]
Answer

Example 2

On a histogram, the bar for the class $15 < h \leq 40$ has a frequency density of $2.8$ . How many values are in this class?

Hint The area of the bar is the frequency: density times width, and the width is

40 - 15 = 25

B2
On a histogram, the bar for the class $35 < w \leq 60$ has a frequency density of $3.2$ . How many values are in this class?
[2 marks]
Answer

Grades 6–7

C1
A bar on a histogram has a frequency density of $2.5$ and stands for $45$ values. The class starts at $10$ . Work out where the class ends.
[2 marks]
Answer
C2
On a histogram, the bar for $0 < t \leq 4$ has a frequency density of $6$ . The bar for $4 < t \leq 10$ has the same frequency. How tall is it?
[2 marks]
Answer

C3
The table gives the frequency density of each bar of a histogram showing the heights of some plants. What percentage of the plants are taller than $30$ cm? Give your answer to $1$ decimal place.
[3 marks]
Answer
C4
A histogram is being drawn. The bar for $20 < w \leq 30$ stands for $42$ values and is $7$ cm tall. The class $30 < w \leq 50$ has a frequency of $36$ . How tall, in cm, should its bar be?
[3 marks]
Answer

Grades 7–8

D1
The table shows the times some people waited for a bus. A histogram is drawn from it. The bar for $10 < t \leq 25$ is twice as tall as the bar for $0 < t \leq 10$ . Work out the value of $x$ . You must show your working.
[3 marks]
Answer

Grade 8 and beyond

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

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out frequency density.
I can read a frequency as a bar's area.
I can estimate part of a class.

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