GCSE Maths · Higher · Chapter 18: Sampling and more complex diagrams · Lesson 3

Cumulative frequency and box plots

Grades 5–7About 50 minutesCalculator allowed35 marks

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NameClassDate

Do Now

Grades 4–6

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

A1
Needed today
6 numbers have a mean of $12$ . What is their total?
[1 mark]
Answer
A2
From chapter 17
Solve $x^{2} < 36$ .
[1 mark]
Answer
A3
Last lesson
On a frequency polygon, the class $30 < x \leq 40$ with frequency 15 is plotted at which point?
[1 mark]
Answer
A4
From chapter 9
A prism has cross-section 17 cm $^{2}$ and length 10 cm. Find its volume.
[1 mark]
Answer

Grades 5–6

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

Example 1

The box plots show the scores of two groups. Compare the two groups.

Hint Compare an average (the median) and a spread (the interquartile range).

B1
The box plots show the scores of two more groups. Compare the two groups.
[3 marks]

Grades 5–6

C1
Write down the cumulative frequencies for the frequencies $9, 17, 28, 19, 7$ .
[2 marks]
Answer
C2
A box plot's five values are $18, 27, 33, 41, 60$ . Work out the interquartile range and the range.
[2 marks]
Answer

C3
Of $70$ times, $44$ are $30$ or less and $59$ are $40$ or less. How many are in $30 < t \leq 40$ , and how many are over $40$ ?
[2 marks]
Answer
C4
The box plot shows the times taken by $200$ runners. Estimate how many of the runners took between $24$ and $35$ minutes.
[2 marks]
Answer
C5
The masses, $m$ g, of 40 apples are grouped as $100 < m \leq 120$ : $6$ , $120 < m \leq 140$ : $14$ , $140 < m \leq 160$ : $12$ , $160 < m \leq 180$ : $8$ . Draw a cumulative frequency graph on the grid.
[3 marks]
C6
The times taken by some runners have a lowest value of 12 minutes, a lower quartile of 19, a median of 24, an upper quartile of 31 and a highest value of 45. Draw a box plot on the scale.
[2 marks]
C7
For $120$ values, at what cumulative frequencies do you read the two quartiles?
[2 marks]
Answer

Grades 6–7

D1
Box plots of test marks: Class A $10, 22, 30, 36, 58$ and Class B $14, 18, 28, 40, 50$ . Ali says, "Class B is more consistent, because its range is smaller."
Is Ali right? Give a reason for your answer.
[3 marks]

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 draw a cumulative frequency graph and read the median and quartiles off it.
I can draw a box plot and read the interquartile range from one.
I can compare two groups by the median and the IQR.

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