Cumulative Frequency & Box Plots Practice Questions

Question 1

4 marks

Do not use a calculator for this question.

The box plot below shows information about the lengths, in minutes, of the phone calls made by Priya in one week.

(a)

Write down the median length of call.

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(b)

Work out the range of the lengths of these calls.

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(c)

Work out the interquartile range of the lengths of these calls.

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Question 2

4 marks

Do not use a calculator for this question.

The grouped frequency table gives information about the masses, in kg, of 50 parcels.

Mass, $m$ (kg)	Frequency
$0 < m \le 1$	8
$1 < m \le 2$	15
$2 < m \le 3$	13
$3 < m \le 4$	9
$4 < m \le 5$	5

(a)

Complete the cumulative frequency table below.

Mass, $m$ (kg)	Cumulative frequency
$0 < m \le 1$	8
$0 < m \le 2$
$0 < m \le 3$
$0 < m \le 4$
$0 < m \le 5$

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(b)

On a grid, draw a cumulative frequency graph for your table.

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(c)

Write down the class interval that contains the median mass.

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Question 3

5 marks

Do not use a calculator for this question.

Here are the numbers of minutes that 15 buses were late arriving at a bus station.

$3 \quad 5 \quad 5 \quad 8 \quad 9 \quad 11 \quad 12 \quad 14 \quad 14 \quad 17 \quad 18 \quad 20 \quad 23 \quad 25 \quad 29$

(a)

Write down the median number of minutes late.

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(b)

Work out the interquartile range of the numbers of minutes late.

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(c)

On a grid with a scale from $0$ to $30$ minutes, draw a box plot for this information.

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Question 4

3 marks

Do not use a calculator for this question.

The box plots show information about the times, in minutes, spent on homework in one evening by a group of Year 10 students and by a group of Year 11 students.

(a)

Write down the upper quartile of the times for the Year 11 students.

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(b)

Compare the distribution of the times for the Year 10 students with the distribution of the times for the Year 11 students.

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Question 0

6 marks

Do not use a calculator for this question.

The table gives information about the amounts of money, in pounds, spent by 100 customers in a garden centre on one Saturday.

Amount spent, $s$ (£)	Frequency
$0 < s \le 10$	12
$10 < s \le 20$	28
$20 < s \le 30$	32
$30 < s \le 40$	18
$40 < s \le 50$	10

(a)

Complete the cumulative frequency table below.

Amount spent, $s$ (£)	Cumulative frequency
$0 < s \le 10$	12
$0 < s \le 20$
$0 < s \le 30$
$0 < s \le 40$
$0 < s \le 50$

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(b)

On a grid, draw a cumulative frequency graph for your table.

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(c)

Use your graph to find an estimate for the median amount of money spent.

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(d)

Use your graph to find an estimate for the interquartile range of the amounts of money spent.

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Question 0

4 marks

Do not use a calculator for this question.

The box plot shows information about the waiting times, in minutes, of the patients at doctors' surgery A on one morning.

The table gives information about the waiting times of the patients at surgery B on the same morning.

	Waiting time (minutes)
Shortest time	5
Lower quartile	12
Median	16
Upper quartile	24
Longest time	45

(a)

On a copy of the grid above, draw a box plot for the information in the table.

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(b)

Compare the distribution of the waiting times at surgery A with the distribution of the waiting times at surgery B.

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Question 0

5 marks

Do not use a calculator for this question.

The cumulative frequency graph gives information about the weights, in grams, of 120 apples.

(a)

Use the graph to find an estimate for the median weight.

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(b)

Work out an estimate for the number of these apples with a weight of more than 155 g.

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(c)

Use the graph to find an estimate for the 90th percentile of the weights.

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Question 0

5 marks

Do not use a calculator for this question.

80 students took a test. The test was marked out of 60. The cumulative frequency graph gives information about their marks.

(a)

Use the graph to find an estimate for the median mark.

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(b)

Use the graph to find an estimate for the interquartile range of the marks.

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(c)

Students who scored more than 45 marks were awarded a merit.

Work out an estimate for the number of these students who were awarded a merit.

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Question 0

6 marks

Do not use a calculator for this question.

60 people each tried to solve a puzzle. The table gives information about the times, $t$ seconds, they took.

Time, $t$ (seconds)	Frequency
$0 < t \le 20$	5
$20 < t \le 40$	13
$40 < t \le 60$	22
$60 < t \le 80$	14
$80 < t \le 100$	6

(a)

Complete the cumulative frequency table below.

Time, $t$ (seconds)	Cumulative frequency
$0 < t \le 20$	5
$0 < t \le 40$
$0 < t \le 60$
$0 < t \le 80$
$0 < t \le 100$

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(b)

On a grid, draw a cumulative frequency graph for your table.

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(c)

The shortest time taken was 5 seconds. The longest time taken was 95 seconds.

Using your graph, draw a box plot for the information about these 60 times.

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Question 0

4 marks

Do not use a calculator for this question.

A gardener grew a large number of tomato plants. He gave fertiliser A to half of the plants and fertiliser B to the other half. The box plots show information about the heights, in cm, of the plants after 4 weeks.

(a)

Work out the interquartile range of the heights of the plants given fertiliser A.

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(b)

Compare the distribution of the heights of the plants given fertiliser A with the distribution of the heights of the plants given fertiliser B.

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(c)

Sam says, "More than half of the plants given fertiliser B are taller than every plant given fertiliser A."

Is Sam correct?
Give a reason for your answer.

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Question 0

5 marks

Do not use a calculator for this question.

30 runners took part in a race. Some information about their times is given below.

The shortest time was 32 minutes.
The range of the times was 41 minutes.
The median time was 48 minutes.
The lower quartile of the times was 42 minutes.
The interquartile range of the times was 14 minutes.

(a)

On a grid with a scale from $30$ to $80$ minutes, draw a box plot for the times of these 30 runners.

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(b)

Work out an estimate for the number of these runners with a time between 48 minutes and 56 minutes.

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Question 0

5 marks

Do not use a calculator for this question.

The table gives information about the distances, in km, travelled to work by the 80 employees of company A.

Distance, $d$ (km)	Frequency
$0 < d \le 5$	14
$5 < d \le 10$	22
$10 < d \le 15$	24
$15 < d \le 20$	12
$20 < d \le 25$	8

The box plot shows information about the distances travelled to work by the employees of company B.

(a)

By drawing a cumulative frequency graph for the information in the table, find an estimate for the median and an estimate for the interquartile range of the distances travelled by the employees of company A.

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(b)

Compare the distribution of the distances travelled by the employees of company A with the distribution of the distances travelled by the employees of company B.

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Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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