1.
80 matches were played in a football tournament. The following table shows the number of
goals scored in all matches.
(a)
Number of goals
0
1
2
3
4
5
Number of matches
16
22
19
17
1
5
Find the mean number of goals scored per match.
(2)
(b)
Find the median number of goals scored per match.
(2)
A local newspaper claims that the mean number of goals scored per match is two.
(c)
Calculate the percentage error in the local newspaper’s claim.
(2)
(Total 6 marks)
2.
The temperatures in °C, at midday in Geneva, were measured for eight days and the results are
recorded below.
7, 4, 5, 4, 8, T, 14, 4
The mean temperature was found to be 7 °C.
(a)
Find the value of T.
(3)
(b)
Write down the mode.
(1)
(c)
Find the median.
(2)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
1
3.
(a)
The exam results for 100 boys are displayed in the following diagram:
0
(b)
10
20
30
40
50
(i)
Find the range of the results.
(ii)
Find the interquartile range.
(iii)
Write down the median.
60
70
80
90
100
The exam results for 100 girls are displayed in the diagram below:
100
number of girls cumulative frequency
90
80
70
60
50
40
30
20
10
0
10
(c)
20
30
40
50
60
exam results
(i)
Write down the median.
(ii)
Find the inter quartile range.
70
80
90
100
Write down the set of results that are the most spread out and give a reason for your
answer.
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
2
4.
The distribution of the weights, correct to the nearest kilogram, of the members of a football
club is shown in the following table.
(a)
Weight (kg)
40 – 49
50 – 59
60 – 69
70 – 79
Frequency
6
18
14
4
On the grid below draw a histogram to show the above weight distribution.
(2)
(b)
Write down the mid-interval value for the 40 – 49 interval.
(1)
(c)
Find an estimate of the mean weight of the members of the club.
(2)
(d)
Write down an estimate of the standard deviation of their weights.
(1)
(Total 6 marks)
8. The numbers of games played in each set of a tennis tournament were
9, 7, 8, 11, 9, 6, 10, 8, 12, 6, 8, 13, 7, 9, 10, 9, 10, 11,
12, 8, 7, 13, 10, 7, 7.
The raw data has been organized in the frequency table below.
games
frequency
6
2
7
5
8
n
9
4
10
4
(a)
Write down the value of n.
(b)
Calculate the mean number of games played per set.
(c)
What percentage of the sets had more than 10 games?
11
2
(d)
What is the modal number of games?
12
2
13
2
(Total 8 marks)
IB Questionbank Mathematical Studies 3rd edition
3
5.
The heights in cm of the members of 4 volleyball teams A, B, C and D were taken and
represented in the frequency histograms given below.
frequency
180
190
height (cm)
frequency
180
frequency
A
200
180
frequency
C
190
height (cm)
200
180
B
190
height (cm)
200
D
190
height (cm)
200
The mean x and standard deviation  of each team are shown in the following table.
I
II
III
IV
x
194
189
188
195

6.50
4.91
3.90
3.74
Match each pair of x and  (I, II, III, or IV) to the correct team (A, B, C or D).
x and 
Team
I
II
III
IV
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
4
The histogram below shows the amount of money spent on food each week by 45 families. The
amounts have been rounded to the nearest 10 dollars.
frequency
6.
18
16
14
12
10
8
6
4
2
0
150
160
170
$
180
190
(a)
Calculate the mean amount spent on food by the 45 families.
(b)
Find the largest possible amount spent on food by a single family in the modal group.
(c)
State which of the following amounts could not be the total spent by all families in the
modal group:
(i) $2430
(ii) $2495
(iii) $2500
(iv) $2520
(v) $2600
(Total 6 marks)
7.
A random sample of 167 people who own mobile phones was used to collect data on the amount
of time they spent per day using their phones. The results are displayed in the table below.
Time spent per
day (t minutes)
Number of people
(a)
0  t 15
15  t  30
30  t  45
45  t  60
60  t  75
75  t  90
21
32
35
41
27
11
State the modal group.
(1)
(b)
Use your graphic display calculator to calculate approximate values of the mean and
standard deviation of the time spent per day on these mobile phones.
(3)
(c)
On graph paper, draw a fully labelled histogram to represent the data.
(4)
(Total 8 marks)
IB Questionbank Mathematical Studies 3rd edition
5
9.
The cumulative frequency graph shows the amount of time in minutes, 200 students spend
waiting for their train on a particular morning.
(a)
Write down the median waiting time.
(1)
(b)
Find the interquartile range for the waiting time.
(2)
The minimum waiting time is zero and the maximum waiting time is 45 minutes.
(c)
Draw a box and whisker plot on the grid below to represent this information.
(3)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
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10.
The weight in kilograms of 12 students in a class are as follows.
63 76 99 65 63 51 52 95 63 71 65 83
(a)
State the mode.
(1)
(b)
Calculate
(i)
the mean weight;
(ii)
the standard deviation of the weights.
(2)
When one student leaves the class, the mean weight of the remaining 11 students becomes
70 kg.
(c) Find the weight of the student who left.
(2)
(Total 5 marks)
11.
The weights in kg, of 80 adult males, were collected and are summarized in the box and whisker
plot shown below.
(a)
Write down the median weight of the males.
(1)
(b)
Calculate the interquartile range.
(2)
(c)
Estimate the number of males who weigh between 61 kg and 66 kg.
(1)
(d)
Estimate the mean weight of the lightest 40 males.
(2)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
7
12. 120 Mathematics students in a school sat an examination. Their scores (given as a percentage)
were summarized on a cumulative frequency diagram. This diagram is given below.
(a)
Complete the grouped frequency table for the students.
Examination
Score x (%)
Frequency
0 ≤ x ≤ 20
20 < x ≤ 40
14
26
40 < x ≤ 60
60 < x ≤ 80
80 < x ≤ 100
(3)
(b)
Write down the mid-interval value of the 40 < x ≤ 60 interval.
(1)
(c)
Calculate an estimate of the mean examination score of the students.
(2)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
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13.
31 pupils in a class were asked to estimate the number of sweets in a jar.
The following stem and leaf diagram gives their estimates.
Stem
Leaf
4
2, 4, 7, 8, 9
5
1, 1, 2, 3, 8, 9
6
0, 2, 2, 4, 6, 6, 7, 8, 8
7
0, 0, 1, 3, 4, 5, 5, 7
8
1, 2, 2
Key: 4 | 7 represents 47 sweets
(a)
For the pupils’ estimates, write down
(i)
the median;
(ii)
the lower quartile;
(iii)
the upper quartile.
(3)
(b)
Draw a box and whisker plot of the pupils’ estimates using the grid below.
(3)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
9
.
(a)
(b)
(c)
0 16  1 22  2 19
80
Note: Award (M1) for substituting correct values into mean
formula.
(M1)
1.75
(A1)
(C2)
An attempt to enumerate the number of goals scored.
(M1)
2
(A1)
2  1.75
× 100
1.75
(M1)
14.3 %
(A1)(ft) (C2)
(C2)
Notes: Award (M1) for correctly substituted % error
formula. % sign not required.
Follow through from their answer to part (a).
If 100 is missing and answer incorrect award (M0)(A0).
If 100 is missing and answer incorrectly rounded award (M1)
(A1)(ft)(AP).
[6]
2.
(a)
7  4  5  4  8  T  14  4
7
8
Note: Award (A1) for sum +T, (A1) for 56 or 7 × 8 or 8 in the
denominator and 7 seen.
(A1)(A1)
T = 10
(A1)
(C3)
(b)
4
(A1)
(C1)
(c)
4, 4, 4, 5, 7, 8, 10, 14
Note: Award (M1) for arranging their numbers in order.
(M1)
Median = 6
(A1)(ft) (C2)
[6]
3.
(a)
(i)
95 – 6 = 89
(ii)
73 – 50 = 23
IB Questionbank Mathematical Studies 3rd edition
(A1)
(A1)
10
(b)
(c)
(iii)
60
(i)
62
(ii)
73 – 43 = 30
(A1)
(C3)
(A1)
(C2)
(R1)
(C1)
(A1)
The girls as the IQR is larger
[6]
4.
Unit penalty (UP) applies in part (c) in this question.
(a)
(A1)(A1)
Note: (A1) for all correct heights, (A1) for all correct end
points (39.5, 49.5 etc.).
Histogram must be drawn with a ruler (straight edge) and
endpoints must be clear.
Award (A1) only if both correct histogram and correct
frequency polygon drawn.
(b)
44.5
(c)
Mean =
UP
(A1)
44.5  6  54.5 18  ...
42
Note: (M1) for a sum of frequencies multiplied by midpoint
values divided by 42.
= 58.3 kg
Note: Award (A1)(A0)(AP) for 58.
(d)
Standard deviation = 8.44
Note: If (b) is given as 45 then award
(b) 45
(c) 58.8 kg
(d) 8.44
(M1)
(A1)(ft) (C2)
(A1)
(A0)
(M1)(A1)(ft) or (C2)(ft) if no working seen.
(C1)
IB Questionbank Mathematical Studies 3rd edition
(C1)
11
(C1)
[6]
5.
x and 
Team
I
B
II
C
III
D
IV
A
(A6)(C6)
Note: Award (A6) for all correct, (A4) for 2 correct or for 3
correct and 1 blank, (A2) for 1 correct but (A0) if the same
letter appears 4 times.
6.
(a)
mean =
(8  150  16  160  11 170  7  180  3  190)
45
(M1)(M1)
Note: Award (M1) for five correct products shown or implied in the
numerator, (M1) for denominator 45.
= $165.78 per week (allow $166)
(A1)(C3)
7
Notes: For 165.7 or 165 award (C3) for exact answer.
9
For 165.77 award (C2) and no (AP).
For 165.77 with no working award (C2)(A0)(AP).
(b)
$164.99 ($165)
(A1)(C1)
(c)
16  $155 = $2480 and 16  164.99 = $2639.84 ($2640)
(M1)
Note: The (M1) is for a sensible attempt to calculate both bounds or
for showing division by 16 of any of the values (i) to (v).
$2430 is not possible
(A1)(ft)(C2)
Note: Follow through if wrong modal group is used in (b).
[6]
7.
Unit penalty (UP) is applicable in question part (b) only.
(a)
45  t < 60
IB Questionbank Mathematical Studies 3rd edition
(A1)1
12
(b)
UP
42.4 minutes
(G2)
21.6 minutes
(G1)3
(c)
(A4)4
[8]
8.
(a)
n=4
(A2)
(b)
Mean number of games is 9.08 (accept 9).
Note: Award (M1) for indicating a sum of games times
frequency (possibly curtailed by dots) or for 227 seen.
(M1)(A1)
(c)
(d)
6 100

= 24%
25 1
Note: Award (M1)(A0) if 6 is replaced by 10. No other
alternative.
Modal number of games is 7.
(M1)(A1)
(A2)
[8]
9.
Unit penalty applies in part (a)
IB Questionbank Mathematical Studies 3rd edition
(C2)
13
(C2)
UP
(a)
Median = 25 mins
(A1)
(C1)
(b)
32 – 16
= 16
(A1)
(A1)(ft) (C2)
Notes: Award (A1) for identifying correct quartiles, (A1)(ft) for
correct answer to subtraction of their quartiles.
(c)
median shown
box with ends at their quartiles
end points at 0 and 45 joined to box with straight lines
Note: Award (A1)(ft)(A1)(ft)(A0) if lines go right through the
box.
(A1)(ft)
(A1)(ft)
(A1) (C3)
[6]
10.
(a)
63 kg
(b)
(i)
70.5 kg
(ii)
14.6 kg (also accept 15.2 kg)
(c)
(A1)1
(G1)
(G1)2
Total weight of 12 students = 846 kg
Total weight of 11 students = 11 × 70 = 770 kg
(M1)
Weight of student who left = 846 – 770 = 76 kg
(A1)2
[5]
11.
Unit penalty applies in parts (a) and (d)
UP
(a)
61 kg
IB Questionbank Mathematical Studies 3rd edition
(A1)
14
(C1)
(b)
66 – 52
= 14
(A1)
(A1)(ft) (C2)
Note: Award (A1) for identifying quartiles, (A1)(ft) for correct
subtraction of their quartiles.
(c)
(d)
UP
20
(A1)
49.5  20  56.5  20
40
Note: Award (M1) for multiplication of midpoints by
frequencies.
(C1)
(M1)
= 53 kg
(A1)
(C2)
[6]
12.
(a)
%
0–20
20–40
40–60
60–80
80–100
F
14
26
58
16
6
(A1)(A1)(A1)
(b)
50
(c)
Mean =
= 45
(A1)
2
3
10 14  ....... 90  6
120
Note: Award (M1) for correct substitution of their values from
(a) in mean formula.
(45.7)
(C1)
(M1)
(A1)(ft) (C2)
[6]
13.
(a)
(i)
66 (sweets)
(ii)
52 (sweets)
(A1)
(iii)
73 (sweets)
(A1)
IB Questionbank Mathematical Studies 3rd edition
(A1)
15
(C3)
Note: If answers to lower and upper quartile are reversed
award (A0) for (ii) and (A1)(ft) for (iii).
(b)
correct median
correct quartiles and box
endpoints at 42 and 82, joined to box by straight lines
Notes: Follow through from their answers to part (a).
Award at most (A1)(ft)(A1)(ft)(A0) if lines go right through the
box.
(A1)(ft)
(A1)(ft)
(A1) (C3)
[6]
IB Questionbank Mathematical Studies 3rd edition
16