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31 questions at your level
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Level 2
Level 3
Level 4
Level 5
Cumulative frequency diagrams
11 questions
Lesson
Not started
Mark as done
40 pupils took a test. The grouped frequency table shows their scores.
Score,
s
s
s
Frequency
0
<
s
≤
10
0 < s \le 10
0
<
s
≤
10
3
10
<
s
≤
20
10 < s \le 20
10
<
s
≤
20
9
20
<
s
≤
30
20 < s \le 30
20
<
s
≤
30
15
30
<
s
≤
40
30 < s \le 40
30
<
s
≤
40
10
40
<
s
≤
50
40 < s \le 50
40
<
s
≤
50
3
(a)
Write down the cumulative frequency for each of the five classes.
(b)
Write down the coordinates of the point that should be plotted for the class
30
<
s
≤
40
30 < s \le 40
30
<
s
≤
40
.
(c)
Explain what the cumulative frequency for the class
20
<
s
≤
30
20 < s \le 30
20
<
s
≤
30
tells you about the pupils' scores.
●●
●●●
Level 2
3 marks
Start
→
Mark as done
The table shows the amounts spent in one week by 80 shoppers at a supermarket.
Amount spent,
x
x
x
(£)
Frequency
0
<
x
≤
20
0 < x \le 20
0
<
x
≤
20
8
20
<
x
≤
40
20 < x \le 40
20
<
x
≤
40
22
40
<
x
≤
60
40 < x \le 60
40
<
x
≤
60
26
60
<
x
≤
80
60 < x \le 80
60
<
x
≤
80
17
80
<
x
≤
100
80 < x \le 100
80
<
x
≤
100
7
(a)
Write down the cumulative frequency for each of the five classes.
(b)
Draw a cumulative frequency diagram for this information.
(c)
Use your diagram to estimate the number of shoppers who spent £50 or less.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The cumulative frequency diagram shows the number of hours that each of 100 students spent revising in one month.
5
10
15
20
25
20
40
60
80
100
Revision time (hours)
Cumulative frequency
(a)
Use the diagram to estimate the number of students who revised for 12 hours or less.
(b)
75
75
75
of the students revised for less than
h
h
h
hours. Use the diagram to estimate the value of
h
h
h
.
(c)
Explain why your answer to part (a) can only be an estimate.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The cumulative frequency graph gives information about the times, in minutes, that
60
60
60
students took to finish a puzzle.
5
10
15
20
25
30
35
40
10
20
30
40
50
60
Time (minutes)
Cumulative frequency
(a)
Use the graph to find an estimate for the median time. (1 mark)
(b)
Use the graph to find an estimate for the interquartile range of the times. (2 marks)
(c)
Use the graph to find an estimate for the number of students who took longer than
25
25
25
minutes. (1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The cumulative frequency graph shows the times, in minutes, taken by
80
80
80
students to travel to school.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Time (minutes)
Cumulative frequency
(a)
Estimate the median time. [1]
(b)
Estimate the interquartile range. [2]
(c)
Estimate the number of students who took longer than
45
45
45
minutes. [1]
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A call centre recorded how long each of 160 customers waited before their call was answered. The cumulative frequency diagram shows the results.
2
4
6
8
10
20
40
60
80
100
120
140
160
Waiting time (minutes)
Cumulative frequency
(a)
Use the diagram to estimate the number of customers who waited between 3 minutes and 7 minutes.
(b)
The call centre claims that 80% of its customers wait less than 6 minutes. Use the diagram to decide whether this claim is correct. You must show your working.
●●●●
●
Level 4
6 marks
Start
→
Mark as done
The table shows the masses of 50 pumpkins grown on a farm.
Mass,
m
m
m
(kg)
Frequency
0
<
m
≤
4
0 < m \le 4
0
<
m
≤
4
4
4
<
m
≤
8
4 < m \le 8
4
<
m
≤
8
11
8
<
m
≤
12
8 < m \le 12
8
<
m
≤
12
18
12
<
m
≤
16
12 < m \le 16
12
<
m
≤
16
12
16
<
m
≤
20
16 < m \le 20
16
<
m
≤
20
5
(a)
Write down the cumulative frequency for each of the five classes.
Bella draws a cumulative frequency diagram for this information. She plots each of her points at the midpoint of its class, so her curve ends at a mass of
18
18
18
kg.
(b)
Explain what Bella's diagram wrongly claims about the heaviest pumpkin.
(c)
Write down the coordinates of the point at which Bella's curve should have ended.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The cumulative frequency diagram shows the heights of 200 trees in a wood.
5
10
15
20
25
50
100
150
200
Height (metres)
Cumulative frequency
(a)
Use the diagram to estimate the median height of the trees.
(b)
Use the diagram to estimate the number of trees that are taller than 12 m.
(c)
Explain why your answer to part (b) is only an estimate.
●●●●
●
Level 4
6 marks
Start
→
Mark as done
The frequency table gives information about the times, in minutes, that
120
120
120
runners took to complete a fun run.
Time (
t
t
t
minutes)
Frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
8
8
8
25
<
t
≤
30
25 < t \le 30
25
<
t
≤
30
22
22
22
30
<
t
≤
35
30 < t \le 35
30
<
t
≤
35
46
46
46
35
<
t
≤
40
35 < t \le 40
35
<
t
≤
40
30
30
30
40
<
t
≤
45
40 < t \le 45
40
<
t
≤
45
14
14
14
(a)
Complete the cumulative frequency table.
Time (
t
t
t
minutes)
Cumulative frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
20
<
t
≤
35
20 < t \le 35
20
<
t
≤
35
20
<
t
≤
40
20 < t \le 40
20
<
t
≤
40
20
<
t
≤
45
20 < t \le 45
20
<
t
≤
45
(1 mark)
(b)
On the grid, draw a cumulative frequency graph for your table.
20
25
30
35
40
45
20
40
60
80
100
120
Time (t minutes)
Cumulative frequency
(2 marks)
(c)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(d)
Use your graph to find an estimate for the number of these runners who took more than
38
38
38
minutes.
(2 marks)
●●●●
●
Level 4
7 marks
Start
→
Mark as done
The cumulative frequency diagram shows the battery life, in hours, of 120 mobile phones.
2
4
6
8
10
20
40
60
80
100
120
Battery life (hours)
Cumulative frequency
(a)
Use the diagram to work out the frequency for each of the classes
0
<
t
≤
2
0 < t \le 2
0
<
t
≤
2
,
2
<
t
≤
4
2 < t \le 4
2
<
t
≤
4
,
4
<
t
≤
6
4 < t \le 6
4
<
t
≤
6
,
6
<
t
≤
8
6 < t \le 8
6
<
t
≤
8
and
8
<
t
≤
10
8 < t \le 10
8
<
t
≤
10
.
(b)
Work out an estimate for the mean battery life.
●●●●●
Level 5
5 marks
Start
→
Mark as done
150 people applied for a job. Each applicant sat a test marked out of 100. The cumulative frequency diagram shows their scores.
20
40
60
80
100
20
40
60
80
100
120
140
Test score
Cumulative frequency
(a)
The 30 applicants with the highest scores will be invited to an interview. Use the diagram to estimate the lowest score an applicant needs in order to be invited to an interview.
(b)
A newspaper claims that more than 40% of the applicants scored 45 or less. Use the diagram to decide whether this claim is correct. You must show your working.
●●●●●
Level 5
6 marks
Start
→
Quartiles & the interquartile range
14 questions
Lesson
Not started
Mark as done
Here are the ages, in years, of the
11
11
11
members of a chess club, written in order:
9
,
11
,
12
,
14
,
14
,
15
,
17
,
18
,
20
,
21
,
26
9, \quad 11, \quad 12, \quad 14, \quad 14, \quad 15, \quad 17, \quad 18, \quad 20, \quad 21, \quad 26
9
,
11
,
12
,
14
,
14
,
15
,
17
,
18
,
20
,
21
,
26
(a)
Write down the median age.
(b)
Work out the interquartile range of the ages.
●●
●●●
Level 2
4 marks
Start
→
Mark as done
For the times taken by
60
60
60
students to complete a puzzle: the shortest time was
5
5
5
minutes, the lower quartile was
12
12
12
minutes, the median was
20
20
20
minutes, the upper quartile was
26
26
26
minutes and the longest time was
41
41
41
minutes.
(a)
Work out the interquartile range. [1]
(b)
How many of the students took
26
26
26
minutes or longer? [1]
A second class had a median of
24
24
24
minutes and an interquartile range of
10
10
10
minutes.
(c)
Compare the times of the two classes. [1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Sasha recorded the time, in seconds, that each of
13
13
13
people took to solve a puzzle. Here are her results:
32
,
18
,
45
,
27
,
21
,
38
,
25
,
30
,
22
,
36
,
28
,
41
,
24
32, \quad 18, \quad 45, \quad 27, \quad 21, \quad 38, \quad 25, \quad 30, \quad 22, \quad 36, \quad 28, \quad 41, \quad 24
32
,
18
,
45
,
27
,
21
,
38
,
25
,
30
,
22
,
36
,
28
,
41
,
24
(a)
Work out the interquartile range of these times.
(b)
Sasha then finds that the time of
45
45
45
seconds was written down wrongly. It should have been
145
145
145
seconds.
State the effect this correction has on the range and on the interquartile range of the times. Give a reason for your answer.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The cumulative frequency diagram shows the time, in minutes, that each of
80
80
80
patients waited to be seen at a clinic.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Waiting time (minutes)
Cumulative frequency
(a)
Use the diagram to estimate the median waiting time.
(b)
Use the diagram to estimate the interquartile range of the waiting times.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The cumulative frequency graph gives information about the times, in minutes, that
60
60
60
students took to finish a puzzle.
5
10
15
20
25
30
35
40
10
20
30
40
50
60
Time (minutes)
Cumulative frequency
(a)
Use the graph to find an estimate for the median time. (1 mark)
(b)
Use the graph to find an estimate for the interquartile range of the times. (2 marks)
(c)
Use the graph to find an estimate for the number of students who took longer than
25
25
25
minutes. (1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The cumulative frequency graph shows the times, in minutes, taken by
80
80
80
students to travel to school.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Time (minutes)
Cumulative frequency
(a)
Estimate the median time. [1]
(b)
Estimate the interquartile range. [2]
(c)
Estimate the number of students who took longer than
45
45
45
minutes. [1]
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The cumulative frequency diagram shows the heights of 200 trees in a wood.
5
10
15
20
25
50
100
150
200
Height (metres)
Cumulative frequency
(a)
Use the diagram to estimate the median height of the trees.
(b)
Use the diagram to estimate the number of trees that are taller than 12 m.
(c)
Explain why your answer to part (b) is only an estimate.
●●●●
●
Level 4
6 marks
Start
→
Mark as done
Class A and class B were each given the same puzzle to solve.
The cumulative frequency diagram shows the time, in seconds, taken by each of the
60
60
60
pupils in class A.
10
20
30
40
50
10
20
30
40
50
60
Time (seconds)
Cumulative frequency
(a)
Use the diagram to estimate the median time for class A.
(b)
Use the diagram to estimate the interquartile range of the times for class A.
(c)
For class B, the median time was
34
34
34
seconds and the interquartile range was
21
21
21
seconds.
Compare the times taken by class A with the times taken by class B.
●●●●
●
Level 4
7 marks
Start
→
Mark as done
Nine numbers are written in order of size:
4
,
7
,
9
,
11
,
14
,
16
,
x
,
21
,
28
4, \quad 7, \quad 9, \quad 11, \quad 14, \quad 16, \quad x, \quad 21, \quad 28
4
,
7
,
9
,
11
,
14
,
16
,
x
,
21
,
28
The interquartile range of the nine numbers is
12
12
12
.
(a)
Write down the median of the nine numbers.
(b)
Work out the value of
x
x
x
.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A shop recorded the amount spent by each of
15
15
15
customers one morning. The amounts, in pounds, were:
12
,
27
,
5
,
17
,
9
,
68
,
14
,
3
,
22
,
8
,
19
,
6
,
24
,
11
,
15
12, \quad 27, \quad 5, \quad 17, \quad 9, \quad 68, \quad 14, \quad 3, \quad 22, \quad 8, \quad 19, \quad 6, \quad 24, \quad 11, \quad 15
12
,
27
,
5
,
17
,
9
,
68
,
14
,
3
,
22
,
8
,
19
,
6
,
24
,
11
,
15
(a)
Work out the interquartile range of the amounts spent.
(b)
Ravi says, "The range of the amounts is £
65
65
65
, so the amounts spent that morning were very spread out."
Explain why the interquartile range gives a more reliable picture of the spread of these amounts than the range does.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The frequency table gives information about the times, in minutes, that
120
120
120
runners took to complete a fun run.
Time (
t
t
t
minutes)
Frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
8
8
8
25
<
t
≤
30
25 < t \le 30
25
<
t
≤
30
22
22
22
30
<
t
≤
35
30 < t \le 35
30
<
t
≤
35
46
46
46
35
<
t
≤
40
35 < t \le 40
35
<
t
≤
40
30
30
30
40
<
t
≤
45
40 < t \le 45
40
<
t
≤
45
14
14
14
(a)
Complete the cumulative frequency table.
Time (
t
t
t
minutes)
Cumulative frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
20
<
t
≤
35
20 < t \le 35
20
<
t
≤
35
20
<
t
≤
40
20 < t \le 40
20
<
t
≤
40
20
<
t
≤
45
20 < t \le 45
20
<
t
≤
45
(1 mark)
(b)
On the grid, draw a cumulative frequency graph for your table.
20
25
30
35
40
45
20
40
60
80
100
120
Time (t minutes)
Cumulative frequency
(2 marks)
(c)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(d)
Use your graph to find an estimate for the number of these runners who took more than
38
38
38
minutes.
(2 marks)
●●●●
●
Level 4
7 marks
Start
→
Mark as done
Ravi measures the lengths, in cm, of some fish caught in a lake in June.
His results are summarised in this table.
Length (cm)
Shortest length
18
18
18
Lower quartile
24
24
24
Median
29
29
29
Interquartile range
9
9
9
Range
26
26
26
(a)
On the grid, draw a box plot to show the information in the table.
June
15
20
25
30
35
40
45
50
Length (cm)
(3 marks)
Ravi also measures the lengths of some fish caught in the lake in September.
He uses his results to draw this box plot.
September
15
20
25
30
35
40
45
50
Length (cm)
(b)
Compare the distribution of the lengths of the fish caught in June with the distribution of the lengths of the fish caught in September.
(2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
During an experiment,
11
11
11
temperatures were recorded in degrees Celsius. For these temperatures:
the median was
20
∘
20\,^{\circ}
20
∘
C
the lower quartile was
14
∘
14\,^{\circ}
14
∘
C
the upper quartile was
29
∘
29\,^{\circ}
29
∘
C
The temperatures are converted to degrees Fahrenheit using
F
=
1.8
C
+
32
F = 1.8C + 32
F
=
1.8
C
+
32
.
(a)
Work out the median of the temperatures in degrees Fahrenheit.
(b)
Work out the interquartile range of the temperatures in degrees Fahrenheit.
●●●●●
Level 5
5 marks
Start
→
Mark as done
A grower has two fields of sunflowers.
For the
120
120
120
sunflowers in field P, the heights have
lower quartile
136
136
136
cm
median
145
145
145
cm
upper quartile
155
155
155
cm
The heights, in centimetres, of a sample of
9
9
9
sunflowers from field Q are
128
,
134
,
140
,
148
,
152
,
157
,
166
,
172
,
195
128, \quad 134, \quad 140, \quad 148, \quad 152, \quad 157, \quad 166, \quad 172, \quad 195
128
,
134
,
140
,
148
,
152
,
157
,
166
,
172
,
195
(a)
Write down the median height of the sample from field Q.
(b)
Work out the interquartile range of the heights of the sample from field Q.
(c)
Estimate how many of the
120
120
120
sunflowers in field P are taller than
155
155
155
cm.
(d)
Compare the heights of the sunflowers in field P with the heights of the sample from field Q.
●●●●●
Level 5
7 marks
Start
→
Box plots
12 questions
Lesson
Not started
Mark as done
The box plot gives information about the masses, in kilograms, of the dogs at a rescue centre.
5
10
15
20
25
30
35
40
Mass (kg)
(a)
Write down the median mass.
(b)
Work out the range of the masses.
(c)
Work out the interquartile range of the masses.
●●
●●●
Level 2
5 marks
Start
→
Mark as done
For the times taken by
60
60
60
students to complete a puzzle: the shortest time was
5
5
5
minutes, the lower quartile was
12
12
12
minutes, the median was
20
20
20
minutes, the upper quartile was
26
26
26
minutes and the longest time was
41
41
41
minutes.
(a)
Work out the interquartile range. [1]
(b)
How many of the students took
26
26
26
minutes or longer? [1]
A second class had a median of
24
24
24
minutes and an interquartile range of
10
10
10
minutes.
(c)
Compare the times of the two classes. [1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A gardener measures the heights of
40
40
40
sunflowers.
The shortest sunflower is
84
84
84
cm tall and the tallest is
186
186
186
cm tall.
The median height is
120
120
120
cm, the lower quartile is
108
108
108
cm and the upper quartile is
156
156
156
cm.
(a)
Draw a box plot for this information.
(b)
Work out the interquartile range of the heights.
(c)
Work out how many of the sunflowers are taller than
156
156
156
cm.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The box plot gives information about the times, in minutes, taken by
200
200
200
people to travel to work.
10
20
30
40
50
60
70
Time (minutes)
(a)
Work out the interquartile range of the times.
(b)
Priya looks at the box plot and says, "Most of these people took between
35
35
35
and
60
60
60
minutes to travel to work, because that part of the box plot is much longer than any other part."
Is Priya correct? Give a reason for your answer.
●●●
●●
Level 3
4 marks
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Mark as done
The box plot shows information about the times, in minutes, that students in class A took to finish a test.
10
20
30
40
50
Time (minutes)
(a)
Write down the interquartile range for class A. (1 mark)
For class B: the shortest time was
12
12
12
minutes, the lower quartile was
20
20
20
minutes, the median was
26
26
26
minutes, the upper quartile was
33
33
33
minutes and the longest time was
40
40
40
minutes.
(b)
Compare the distribution of the times for class A with the distribution of the times for class B. (2 marks)
(c)
What fraction of the students in class A took longer than
30
30
30
minutes? (1 mark)
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Level 3
4 marks
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Mark as done
The box plots give information about the marks scored in the same test by the students at School P and by the students at School Q.
School P:
10
20
30
40
50
60
70
Mark
School Q:
10
20
30
40
50
60
70
Mark
(a)
Compare the distribution of the marks at School P with the distribution of the marks at School Q.
(b)
160
160
160
students at School P took the test. Work out how many of them scored more than
50
50
50
marks.
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Level 4
4 marks
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Mark as done
The box plot gives information about the times, in minutes, that
80
80
80
customers spent in a café one afternoon. One of the times is shown as a cross.
10
20
30
40
50
60
70
80
Time (minutes)
(a)
Write down the longest of these times that is
not
an outlier.
(b)
Work out the interquartile range of the times.
(c)
Zak says, "The range of these times is
35
35
35
minutes."
Explain why Zak is wrong.
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Level 4
4 marks
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Mark as done
The cumulative frequency graph gives information about the marks scored by
80
80
80
students in a test.
10
20
30
40
50
60
70
10
20
30
40
50
60
70
80
Mark
Cumulative frequency
The lowest mark scored was
12
12
12
and the highest mark scored was
68
68
68
.
(a)
Use the graph to draw a box plot for the marks.
(b)
Work out the interquartile range of the marks.
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Level 4
4 marks
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Mark as done
Ravi measures the lengths, in cm, of some fish caught in a lake in June.
His results are summarised in this table.
Length (cm)
Shortest length
18
18
18
Lower quartile
24
24
24
Median
29
29
29
Interquartile range
9
9
9
Range
26
26
26
(a)
On the grid, draw a box plot to show the information in the table.
June
15
20
25
30
35
40
45
50
Length (cm)
(3 marks)
Ravi also measures the lengths of some fish caught in the lake in September.
He uses his results to draw this box plot.
September
15
20
25
30
35
40
45
50
Length (cm)
(b)
Compare the distribution of the lengths of the fish caught in June with the distribution of the lengths of the fish caught in September.
(2 marks)
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Level 4
5 marks
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The table gives some information about the lengths, in minutes, of
60
60
60
films shown at a film festival.
Length (minutes)
Shortest length
84
84
84
Longest length
152
152
152
Lower quartile
97
97
97
Upper quartile
121
121
121
Median
108
108
108
(a)
Draw a box plot to represent this information.
80
90
100
110
120
130
140
150
160
Length (minutes)
(3 marks)
(b)
Work out an estimate for the number of these films with a length between
97
97
97
minutes and
121
121
121
minutes.
(1 mark)
Oscar says,
"The median is
108
108
108
minutes, so one of the films must be exactly
108
108
108
minutes long."
(c)
Is Oscar correct? Give a reason for your answer.
(1 mark)
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Level 4
5 marks
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Mark as done
The box plots give information about the distances, in km, travelled to work by the employees at two companies.
Company A, which has
200
200
200
employees:
10
20
30
40
50
60
Distance (km)
Company B, which has
120
120
120
employees:
10
20
30
40
50
60
Distance (km)
(a)
Work out how many of the employees at Company A travel more than
30
30
30
km to work.
(b)
Jordan says, "The box for Company B is much wider than the box for Company A, so more employees at Company B travel a distance between their own company's lower quartile and upper quartile."
Is Jordan correct? You must show your working.
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Level 5
5 marks
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Mark as done
Sam is drawing a box plot for a set of data. He knows that
the smallest value is
9
9
9
,
the range is
46
46
46
,
the median is
34
34
34
,
the interquartile range is
18
18
18
,
the median is
7
7
7
more than the lower quartile.
(a)
Work out the largest value.
(b)
Work out the lower quartile.
(c)
Work out the upper quartile.
(d)
Sam says that the same number of values lie between the lower quartile and the median as lie between the upper quartile and the largest value.
Is Sam correct? Give a reason for your answer.
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Level 5
6 marks
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→