PLC Papers
Created For:
Year 11 Topic Practice Paper: Cumulative Frequency and Box Plots
Boxplots 1
Objective:
Grade 6
Interpret and construct box plots
Question 1
The box plot gives information about the weights of a group of children.
(a) Write down the median.
………………………………… kg
(1)
………………………………… kg
(2)
(b) Work out the interquartile range.
There are 80 children in the group.
(c) Work out an estimate for the number of children who weigh 32 kg or more.
……………………………………
(2)
(Total 5 marks)
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Question 2
The data in the table below represents the ages of a football team.
23
21
25
26
25
28
30
42
51
24
36
(a) Work out the median.
…………………………………… years
(1)
…………………………………… years
(2)
(b) Work out the interquartile range.
(c) Draw a boxplot to represent this data
(2)
(Total 5 marks)
Total marks /10
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Boxplots 2
Objective:
Grade 6
Interpret and construct box plots
Question 1
Dave recorded the length of time 24 pupils took to solve a puzzle.
The table shows information about these times in minutes.
(a) Work out the number of teachers with a travel time of 3.4 minutes or more.
…………………… …………
(b) On the grid, draw a box plot to show the information in the table.
(2)
(Total 4 marks)
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(2)
Question 2
Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below.
(a) Use the boxplot to fill in the values in this summary table:
(3)
(b) Calculate the Inter Quartile Range (IQR).
………………………………
(2)
(c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median?
Decrease □
Stay the same □
Increase□
(1)
(Total 6 marks)
Total marks /10
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Boxplots 3
Objective:
Grade 6
Interpret and construct box plots
Question 1
The following data represents the temperature in the first 15 days of June (Set 1) and the second 15 days of June
(Set 2).
Draw suitable charts to represent the data.
(Total 6 marks)
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Question 2
The boxplots below show the results of two sets of test scores from Class 1 and Class 2.
(a) Make two comparisons between the two sets of data.
(i)
……………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………
(ii)
……………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………
(Total 4 marks)
Total marks /10
PiXL PLC 2017 Certification
Boxplots 4
Objective:
Grade 6
Interpret and construct box plots
Question 1
The heights of 3 year olds in two towns (Mathtown and Algebraville) were measure. The data for these is found
below:
Compare the heights of the 3 year olds in these towns.
(i)
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
(ii)
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
(10)
Total marks /10
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Cumulative Frequency 1
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data)
Question 1
The grouped frequency table shows information about the weekly wages of 80 factory workers.
(a) Complete the cumulative frequency table.
(1)
(b) On the next page, draw a cumulative frequency graph for your table.
(2)
PiXL PLC 2017 Certification
90
80
CUMULATI VE FREQUENCY
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
700
800
WEEKLY WAGE, £
(c) Use your graph to find an estimate for the median.
……………………………………
(1)
(d) Use your graph to find an estimate for the interquartile range.
……………………………………
(2)
(e) Use your graph to find an estimate for the number of workers with a weekly wage of more than £530.
……………………………………
(2)
(Total 8 marks)
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Question 2
The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.
(a) Use the graph to find an estimate for the median time.
……………………………………
(1)
(b) Use the graph to find an estimate for the lower quartile..
……………………………………
(1)
(Total 2 marks)
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 2
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous
data)
Question 1
The table below shows information about the heights of 60 students.
(a)
On the grid, draw a cumulative frequency graph for the information in the table.
(3)
60
CUMULATI VE FREQUENCY
50
40
30
20
10
0
140
150
160
170
TI ME, T SECS
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180
190
200
(b)
Find an estimate
(i) for the median,
........................................................................................................................................................
(ii) for the interquartile range.
........................................................................................................................................................
(3)
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2
The table shows information about the lengths, in seconds, of 40 TV adverts.
(a) Complete the cumulative frequency table for this information.
(1)
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(b) On the grid, draw a cumulative frequency graph for your table.
(2)
45
40
CUMULATI VE FREQUENCY
35
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
TI ME, T SECS
(c) Use your graph to find an estimate for the median length of these TV adverts.
……………………… seconds
(1)
(Total 4 marks)
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 3
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data)
Question 1
The table below shows the times it takes a group of boys to run 150m.
Boys time, secs
Frequency
0
<x≤
5
0
5
<x≤
10
2
10
<x≤
15
7
15
<x≤
20
16
20
<x≤
25
9
25
<x≤
30
2
Totals
36
The cumulative frequency graph below shows the times it takes a group of girls to run 150m.
45
40
CUMULATI VE FREQUENCY
35
30
25
20
15
10
5
0
0
5
10
15
20
TI ME, SECS
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25
30
35
(a) Which is the quicker gender at running 150m. Explain your answer.
……………………………………….
(1)
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
(5)
b)
Were the boys or the girls more consistent in their running speeds, explain your reasons for your answer
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
(4)
Total for question - 10
marks
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 4
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous
data)
Question 1
The cumulative frequency below shows the scores of two classes (X and Y) in a maths assessment which is out of 90
marks.
30
Class X
25
CUMULATI VE FREQUENCY
Class Y
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
100
TEST SCORES
a)
(i) Which set do you think is the Higher set?
………………………………………….
(1)
(ii) Explain your answer
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
(2)
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b)
Which class is more consistent? Explain your answer.
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
(4)
c) The pass mark for the test was 63%. How many students in total (from both classes) failed?
………………………………………….
(3)
Total marks /10
PiXL PLC 2017 Certification
PLC Papers
Created For:
Year 11 Topic Practice Paper: Cumulative Frequency and Box Plots
Boxplots 1
Objective:
Grade 6
SOLUTIONS
Interpret and construct box plots
Question 1
The box plot gives information about the weights of a group of children.
(a) Write down the median.
………………28………A1………… kg
(1)
(b) Work out the interquartile range.
32 – 25 = (7)
M1
………………7………A1………… kg
(2)
There are 80 children in the group.
(c) Work out an estimate for the number of children who weigh 32 kg or more.
25% of 80 = (20)
M1
……………20…………A1……………
(Total 5 marks)
Question 2
The data in the table below represents the ages of a football team.
23
21
25
26
25
28
30
42
51
24
36
(a) Work out the median.
………………26…………A1………… years
(1)
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(2)
(b) Work out the interquartile range.
36 – 24 = 12
M1
…………………12…A1……………… years
(2)
(c) Draw a boxplot to represent this data
(2)
(Total 5 marks)
Total marks /10
PiXL PLC 2017 Certification
Boxplots 2
Objective:
Grade 6
SOLUTIONS
Interpret and construct box plots
Question 1
Dave recorded the length of time 24 pupils took to solve a puzzle.
The table shows information about these times in minutes.
(a) Work out the number of teachers with a travel time of 3.4 minutes or more.
75% of 24 = (18)
M1
……………18………A1…………
(2)
(b) On the grid, draw a box plot to show the information in the table.
(2)
(Total 4 marks)
PiXL PLC 2017 Certification
Question 2
Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below.
(a) Use the boxplot to fill in the values in this summary table:
Length, cms
Minimum
24
Lower Quartile
38
Median
40
Upper quartile
46
Maximum
54
(3)
(b) Calculate the Inter Quartile Range (IQR).
46 – 38 = (8)
M1
……………8………A1…………
(2)
(c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median?
Decrease □
Stay the same 
Increase□
(1)
(Total 6 marks)
Total marks /10
PiXL PLC 2017 Certification
Boxplots 3
Objective:
Grade 6
SOLUTIONS
Interpret and construct box plots
Question 1
The following data represents the temperature in the first 15 days of June (Set 1) and the second 15 days of June
(Set 2).
Draw suitable charts to represent the data.
Set 1
Set 2
Minimum
18
21
Lower Quartile
21
25
Median
23
27
Upper Quartile
27
29
Maximum
29
34
Choosing to use a boxplot
C1
Calculate summary data
A3
Draw boxplots
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A2
(Total 6 marks)
Question 2
The boxplots below show the results of two sets of test scores from Class 1 and Class 2.
(a) Make two comparisons between the two sets of data.
(i)
…Set 2 have scored better (Contextual answer - C1) in the test overall as the median is higher
(Compare medians - C1)
……………………………………………………………………………………………………………………………………………………
(ii)
…Set 2 scores are much more spread out (contextual answer – C1, the range (or IQR) is higher in
set 2 (compare IQR or Range – C1)
……………………………………………………………………………………………………………………………………………………
(Total 4 marks)
Total marks /10
PiXL PLC 2017 Certification
Boxplots 4
Objective:
Grade 6
SOLUTIONS
Interpret and construct box plots
Question 1
The heights of 3 year olds in two towns (Mathtown and Algebraville) were measure. The data for these is found
below:
Mathtown
Algebraville
Minimum
0.8
0.9
Lower Quartile
0.9
1.1
Median
1.2
1.2
Upper Quartile
1.35
1.35
Maximum
1.4
1.5
Calculate summary values for Mathtown - A3
IQR = 0.45
Median = 1.2
Range = 0.6
Write down summary values for Algebraville or draw a Boxplot for Mathtown– A3
IQR = 0.6
Median = 1.2
Range = 0.6
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Compare the heights of the 3 year olds in these towns.
(i)
…The two towns are very similar in the spread of heights (range is the same). IQR is slightly larger
in MathTown (C2)
……………………………………………………………………………………………………………………………………………………
(ii)
…The children are taller (C1 – Contextual answer) in Algebraville as all data values except median
are higher (C1)
……………………………………………………………………………………………………………………………………………………
(4)
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 1
Grade 6
SOLUTIONS
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data)
Question 1
The grouped frequency table shows information about the weekly wages of 80 factory workers.
(a) Complete the cumulative frequency table.
(1)
(b) On the next page, draw a cumulative frequency graph for your table.
(2)
PiXL PLC 2017 Certification
90
80
CUMULATI VE FREQUENCY
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
700
800
WEEKLY WAGE, £
(c) Use your graph to find an estimate for the median.
…………360…………B1……… (1)
(d) Use your graph to find an estimate for the interquartile range.
440 – 285 = (155)
M1
……………155…………A1…………
(2)
(e) Use your graph to find an estimate for the number of workers with a weekly wage of more than £530.
Read off graph 73
M1
80 – 73 = (7)
……………7…………B1…………… (2)
(Total 8 marks)
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Question 2
The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.
(a) Use the graph to find an estimate for the median time.
………68…………A1……………
(1)
(b) Use the graph to find an estimate for the lower quartile.
………53……………A1…………… (1)
(Total 2 marks)
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 2
SOLUTIONS
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous
data)
Question 1
The table below shows information about the heights of 60 students.
(a)
On the grid, draw a cumulative frequency graph for the information in the table.
(3)
70
CUMULATI VE FREQUENCY
60
50
40
30
20
10
0
140
150
160
170
HEI GHT, CMS
PiXL PLC 2017 Certification
180
190
200
(b)
Find an estimate
(i) for the median,
.............................172.........................A1..................................................................................................
(ii) for the interquartile range.
....................177 – 165 = (12).........M1
A1
(3)
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2
The table shows information about the lengths, in seconds, of 40 TV adverts.
(a) Complete the cumulative frequency table for this information.
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
PiXL PLC 2017 Certification
(2)
45
CUMULATI VE FREQUENCY
40
35
30
25
20
15
10
5
0
0
10
20
30
40
TI ME, T SECS
50
60
70
(c) Use your graph to find an estimate for the median length of these TV adverts.
………37……B1………… seconds
(Total 4 marks)
Total marks /10
PiXL PLC 2017 Certification
(1)
Cumulative Frequency 3
Grade 6
SOLUTIONS
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data)
Question 1
The table below shows the times it takes a group of boys to run 150m.
Boys time, secs
Cumulative
Frequency
Boys time, secs
Frequency
0
<x≤
5
0
0
<x≤
5
0
5
<x≤
10
2
0
<x≤
10
2
10
<x≤
15
7
0
<x≤
15
9
15
<x≤
20
16
0
<x≤
20
25
20
<x≤
25
9
0
<x≤
25
34
25
<x≤
30
2
0
<x≤
30
36
Totals
36
The cumulative frequency graph below shows the times it takes a group of girls to run 150m.
45
40
CUMULATI VE FREQUENCY
35
30
25
20
15
10
5
0
0
5
10
15
20
TI ME, SECS
PiXL PLC 2017 Certification
25
30
35
(a) Which is the quicker gender at running 150m. Explain your answer.
……………………………………….
(1)
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
(5)
M1 finding the cumulative frequency of the boys
M1A1 Drawing the cumulative frequency curve for the boys
A1 find the median for the boys
18
A1 find the median for the girls
18.5
b)
Were the boys or the girls more consistent in their running speeds, explain your reasons for your answer
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………………….
(4)
Calculate the upper and lower quartile for boys and girls
Calcualate the interquartile range for boys and girls
M2
A1
Boys IQR = 21-15 = 6
Girls IQR = 24-17 = 7
State the more consistent due to having a smaller IQR C1
Boys
Total for question – 10 marks
Total marks /10
PiXL PLC 2017 Certification
Cumulative Frequency 4
SOLUTIONS
Grade 6
Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous
data)
Question 1
The cumulative frequency below shows the scores of two classes (X and Y) in a maths assessment which is out of 90
marks.
30
Class X
25
CUMULATI VE FREQUENCY
Class Y
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
100
TEST SCORES
a) (i) Which set do you think is the Higher set?
…………Class Y………………A1……………….
(1)
(ii) Explain your answer
………………The median score in class X was 49 whilst the median score in class Y was 63 which means class
Y did better………………………………………………………B2 – Finding the medians …………………………………………………
………………………………………………………………………………………………………………………………………………………………………
(2)
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b)
Which class is more consistent? Explain your answer.
………IQR class X = 56 – 40 = (16)………………………………………………………………………………………………………………………
………IQR class Y = 70 – 52 = (18)…………………………M1A1…………………………………………………………………………………
………Class X is more consistent as the IQR is smaller and therefore lower spread.…………………..
……………………A1…………Correct class………C1 ……………Reference to IQR/spread of data………………………………..
(4)
c) The pass mark for the test was 63%. How many students in total (from both classes) failed?
63/100 x 90 = 57 marks
B1
9 + 23 = (49)
M1
……………32…………A1………………….
(3)
Total marks /10
PiXL PLC 2017 Certification