StatisticsCambridge IGCSE Maths: Topic test

20 questions, 52 marks

Cambridge IGCSE Maths

Statistics topic test

Total 52 marks

Name

Class

Date

1
A fitness tracker recorded the number of steps (in thousands) taken by 9 employees during a lunchtime walk: 7, 3, 7, 5, 9, 4, 7, 6, 1.
(a)
What is the modal number of steps (in thousands)?
[1 mark]
A7
B1
C6
D9
(b)
What is the median number of steps (in thousands)?
[1 mark]
A4
B6
C7
D9
(c)
What is the range of the number of steps (in thousands)?
[1 mark]
A6
B7
C8
D9
Total for question 1: 3 marks
2
A school recorded attendance at three after-school clubs (Art, Chess, Drama) each day for 5 days using a composite bar chart. The total attendance each day was: Monday 24, Tuesday 30, Wednesday 18, Thursday 26, Friday 32. Across the week, Art had 60 attendances in total and Chess had 45.
(a)
Calculate the total attendance across the week for all three clubs, then find the number of attendances that were at Drama club.
[2 marks]
(b)
Given Drama had 25 attendances across the week, calculate what percentage of the week's total attendance was at Drama, giving your answer correct to 1 decimal place.
[2 marks]
Total for question 2: 4 marks
3
A call centre recorded the duration, in minutes, of 90 calls taken during one shift, grouped into classes of unequal width: 0 <= t < 5 (width 5) has frequency density 4; 5 <= t < 10 (width 5) has frequency density 6; 10 <= t < 30 (width 20) has frequency density 2.
(a)
Calculate the number of calls in each of the three classes, and hence find how many calls lasted less than 10 minutes.
[3 marks]
(b)
Given that a call is charged at a flat rate only if it lasts 10 minutes or more, calculate the percentage of the 90 calls that were charged at the flat rate, correct to 1 decimal place.
[3 marks]
Total for question 3: 6 marks
4
In a long jump competition, the distances jumped, in metres, by 60 athletes were recorded in a cumulative frequency table: fewer than 3 m - 4 athletes; fewer than 4 m - 16 athletes; fewer than 5 m - 40 athletes; fewer than 6 m - 54 athletes; fewer than 7 m - 60 athletes.
(a)
Use the cumulative frequency table to estimate the median distance jumped, and estimate the interquartile range.
[4 marks]
(b)
Estimate the mean distance jumped by the 60 athletes, using the midpoint of each class (classes: 0-3 m, 3-4 m, 4-5 m, 5-6 m, 6-7 m, with frequencies 4, 12, 24, 14, 6).
[4 marks]
(c)
The mean distance jumped by a second group of 40 athletes was 4.20 m, and their interquartile range was 0.90 m. Calculate the combined mean distance jumped by all 100 athletes in both groups, and state, with a reason, which group had the more consistent (less spread) distances.
[5 marks]
Total for question 4: 13 marks
5
A gym trainer recorded, for 8 members, the number of hours of exercise per week (x) and their resting heart rate in beats per minute (y): (2, 78), (3, 74), (4, 70), (5, 68), (6, 64), (7, 60), (8, 58), (9, 55).
(a)
What type of correlation is shown between hours of exercise per week and resting heart rate?
[1 mark]
Astrong positive
Bno correlation
Cweak positive
Dstrong negative
(b)
A line of best fit for this data has equation y = -3x + 84. Using this line, estimate the resting heart rate for a member who exercises for 10 hours per week.
[1 mark]
A54
B51
C57
D60
(c)
Using the same line of best fit y = -3x + 84, estimate the number of hours of exercise per week for a member with a resting heart rate of 69 bpm.
[1 mark]
A3
B5
C6
D7
Total for question 5: 3 marks
6
The waiting times, in minutes, of 15 patients at a clinic are shown in an ordered stem-and-leaf diagram (key: 1 | 4 means 14 minutes): Stem 0: leaves 5, 8, 9. Stem 1: leaves 0, 2, 4, 4, 7, 9. Stem 2: leaves 1, 3, 5, 8. Stem 3: leaves 2, 6.
(a)
Find the median waiting time.
[2 marks]
(b)
Find the interquartile range of the waiting times.
[2 marks]
Total for question 6: 4 marks
7
The number of emails received in a day by 40 office employees was recorded in a grouped frequency table: 0 <= e < 10 - 6 employees; 10 <= e < 20 - 14 employees; 20 <= e < 30 - 12 employees; 30 <= e < 40 - 5 employees; 40 <= e < 50 - 3 employees.
(a)
Write down the modal class, and calculate an estimate of the mean number of emails received per employee.
[3 marks]
(b)
An employee is classed as 'high volume' if they receive 30 or more emails a day. Calculate the percentage of employees who are high volume, and state whether the mean (21.25) or the modal class (10 <= e < 20) better represents a 'typical' employee, giving a reason.
[3 marks]
Total for question 7: 6 marks
8
A histogram represents the ages, in years, of 120 members of a cycling club, using unequal class widths: 10 <= a < 20 (width 10) has frequency density 3; 20 <= a < 25 (width 5) has frequency density 8; 25 <= a < 40 (width 15) has frequency density 2; 40 <= a < 60 (width 20) has frequency density 1.
(a)
Calculate the frequency for each of the four classes, and hence find the total number of members aged under 25.
[4 marks]
(b)
Using the midpoint of each class, estimate the mean age of the 120 members.
[4 marks]
(c)
The cycling club wants to compare age spread with a running club, whose members have a mean age of 31.4 years and a range of 38 years. The cycling club's oldest member is 58 and youngest is 12. Calculate the cycling club's range, and comment on which club has members of more similar age to each other, and which club is older on average.
[5 marks]
Total for question 8: 13 marks

End of questions