Averages from Frequency Tables: Fluency and Exam Drill - Worksheets, Questions and Revision

22 original exam-style questions - 9 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 10)
« Previous: Averages from Frequency TablesNext: Probability »
Revision Library
revisionlibrary.co.uk
GCSE · Statistics: averages and range

4.18D Averages from Frequency Tables: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 70 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Priya asked 20 pupils in her class how many siblings they have. The table shows her results.

Number of siblings (x): 0, 1, 2, 3, 4
Frequency (f): 6, 9, 3, 1, 1
Total number of pupils = 20

Write down the mode of the number of siblings.
(Total for Question 1 is 1 mark)
2
A hockey team's coach recorded the number of goals scored in each of 15 matches. The table shows the results.

Goals scored (x): 0, 1, 2, 3, 4
Frequency (f): 2, 5, 4, 3, 1
Total number of matches = 15

Write down the range of the number of goals scored.
(Total for Question 2 is 1 mark)
3
Callum recorded the number of text messages sent by 17 students during one evening. The table shows the results.

Messages sent (x): 0, 1, 2, 3, 4, 5
Frequency (f): 1, 3, 5, 4, 3, 1
Total number of students = 17

Find the median number of messages sent.
(Total for Question 3 is 2 marks)
4
Grace kept a record of the number of books read last month by 20 pupils in her form. The table shows the results.

Books read (x): 0, 1, 2, 3, 4
Frequency (f): 3, 7, 6, 3, 1
Total number of pupils = 20

Find the median number of books read.
(Total for Question 4 is 2 marks)
5
The table shows the number of pets owned by 10 pupils.

Number of pets (x): 0, 1, 2, 3
Frequency (f): 4, 3, 2, 1
Total number of pupils = 10

Work out the mean number of pets owned.
(Total for Question 5 is 2 marks)
6
24 pupils were asked how many siblings they have. One frequency, a, is missing from the table.

Number of siblings (x): 0, 1, 2, 3
Frequency (f): 5, a, 6, 2
Total number of pupils = 24

Find the value of a.
(Total for Question 6 is 2 marks)
7
A school recorded the time, t minutes, spent on homework by 30 pupils in one evening. The table shows the results.

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2
Total number of pupils = 30

Write down the modal class.
(Total for Question 7 is 1 mark)
8
Using the same table as Question 7 (time, t minutes, spent on homework by 30 pupils):

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2
Total number of pupils = 30

State the class that contains the median.
(Total for Question 8 is 2 marks)
9
Using the same table as Questions 7 and 8:

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2

Write down the midpoint of the class 20 < t ≤ 40.
(Total for Question 9 is 1 mark)
10
Using the same table as Questions 7 to 9 (time, t minutes, spent on homework by 30 pupils):

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2
Total number of pupils = 30

Calculate an estimate for the mean time spent on homework.
(Total for Question 10 is 3 marks)
11
Using the same table as Questions 7 to 10 (time, t minutes, spent on homework by 30 pupils):

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2

Find an estimate for the range of the times, using the class boundaries.
(Total for Question 11 is 2 marks)
12
Using the same table as Questions 7 to 11 (time, t minutes, spent on homework by 30 pupils):

Time, t (minutes): 0 < t ≤ 20, 20 < t ≤ 40, 40 < t ≤ 60, 60 < t ≤ 80, 80 < t ≤ 100
Frequency (f): 4, 9, 11, 4, 2

Write down the class width of the class 60 < t ≤ 80.
(Total for Question 12 is 1 mark)
13
The table shows the number of aces served by a tennis player in 10 games.

Aces served (x): 0, 1, 2, 3, 4
Frequency (f): 2, 4, 2, 1, 1
Total number of games = 10

Work out the mean number of aces per game.
(Total for Question 13 is 2 marks)
14
A delivery firm recorded the mass, m kg, of 25 parcels. The table shows the results.

Mass, m (kg): 0 < m ≤ 5, 5 < m ≤ 10, 10 < m ≤ 15, 15 < m ≤ 20, 20 < m ≤ 25
Frequency (f): 6, 10, 6, 2, 1
Total number of parcels = 25
(a)Write down the modal class.(1)
(b)State the class that contains the median.(1)
(Total for Question 14 is 2 marks)
15
24 pupils were asked how many siblings they have, but the table has been damaged and one frequency, a, is unknown.

Number of siblings (x): 0, 1, 2, 3
Frequency (f): 2, 4, a, 1

Given that the mean number of siblings is 1.3, find the value of a. You must show your working.
(Total for Question 15 is 4 marks)
16
20 pupils in Class A sat a test out of 40. The table shows their scores, s.

Score, s: 0 < s ≤ 10, 10 < s ≤ 20, 20 < s ≤ 30, 30 < s ≤ 40
Frequency (f): 2, 5, 9, 4
Total number of pupils = 20
(a)Calculate an estimate for the mean score for Class A.(3)
(b)20 pupils in Class B sat the same test. Their estimated mean score was 27. Compare the performance of the two classes, referring to your answer to part (a).(1)
(Total for Question 16 is 4 marks)
17
A cafe recorded the time, m minutes, that 26 + b customers spent queuing at the counter. One frequency, b, is unknown.

Time, m (minutes): 0 < m ≤ 5, 5 < m ≤ 10, 10 < m ≤ 15, 15 < m ≤ 20
Frequency (f): 8, 12, b, 6

Given that the estimated mean queuing time is 10 minutes, find the value of b. You must show your working.
(Total for Question 17 is 4 marks)
18
30 pupils were asked how many hours of TV they watched last night. The table shows the results, but one frequency, c, is missing.

Hours watched (x): 0, 1, 2, 3, 4
Frequency (f): 6, 10, c, 4, 2
Total number of pupils = 30
(a)Find the value of c.(2)
(b)Write down the modal number of hours watched.(1)
(c)Find the median number of hours watched.(2)
(Total for Question 18 is 5 marks)
19
The table shows the annual salary, in thousands of pounds, of 10 employees at a small company.

Salary, s (GBP thousands): 20 ≤ s < 30, 30 ≤ s < 40, 40 ≤ s < 50, 50 ≤ s < 60, 200 ≤ s < 210
Frequency (f): 3, 4, 1, 1, 1
Total number of employees = 10
(a)Calculate an estimate for the mean salary.(3)
(b)State the class containing the median, and explain why the median might be a more suitable measure than the mean to describe a typical salary at this company.(2)
(Total for Question 19 is 5 marks)
20
25 learner drivers were asked how many driving lessons they took before passing their test. Two frequencies, p and q, are missing.

Number of lessons: 10-19, 20-29, 30-39, 40-49
Frequency (f): 4, p, q, 3
Total number of learner drivers = 25

Given that the modal class is 20-29, work out a possible pair of values for p and q, and give a reason for your answer.
(Total for Question 20 is 4 marks)
21
20 members of a gym class each completed a number of pull-ups in one minute. Two frequencies, p and q, are missing from the table.

Pull-ups completed (x): 2, 3, 4, 5, 6
Frequency (f): 2, p, q, 4, 1
Total number of members = 20

Given that the mean number of pull-ups is 3.9, find the values of p and q. You must show your working.
(Total for Question 21 is 6 marks)
22
A competition weighed 60 fish and recorded their length, l cm, in a grouped frequency table. Two of the frequencies are given in terms of n.

Length, l (cm): 0 < l ≤ 20, 20 < l ≤ 40, 40 < l ≤ 60, 60 < l ≤ 80
Frequency (f): n, 3n, 18, 2n
Total number of fish = 60
(a)Find the value of n.(2)
(b)Using your value of n, calculate an estimate for the mean length of the fish.(4)
(Total for Question 22 is 6 marks)
Mark scheme · 4.18D Averages from Frequency Tables: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22