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

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GCSE · Statistics

S03D Averages from a Frequency Table: Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The number of magazines bought by 12 customers in a shop is shown below.

Magazines bought	1	2	3
Frequency	5	4	3

Write down the modal number of magazines bought.

(Total for Question 1 is 1 mark)

The number of siblings reported by each pupil in a class is shown below.

Siblings	0	1	2	3
Frequency	4	5	3	2

Work out how many pupils were surveyed in total.

(Total for Question 2 is 1 mark)

State whether this is True or False: The modal value in a frequency table is the value with the highest frequency.

(Total for Question 3 is 1 mark)

Which calculation correctly finds the mean from a frequency table?

A) sum(x) divided by n
B) sum(f times x) divided by sum(f)
C) sum(f) divided by sum(x)
D) sum(f times x) divided by the number of different values

A) sum(x) divided by n
B) sum(f times x) divided by sum(f)
C) sum(f) divided by sum(x)
D) sum(f times x) divided by the number of different values

(Total for Question 4 is 1 mark)

The shoe sizes of 11 customers in a shop are shown below.

Shoe size	5	6	7
Frequency	3	5	3

Find the median shoe size.

(Total for Question 5 is 2 marks)

The number of pets owned by 12 families is shown below.

Pets owned	0	1	2	3
Frequency	4	5	2	1

Work out the median number of pets owned.

(Total for Question 6 is 2 marks)

The number of texts sent in one evening by 10 students is shown below.

Texts sent	0	1	2	3
Frequency	2	3	4	1

Calculate the mean number of texts sent.

(Total for Question 7 is 2 marks)

A hockey team recorded the number of goals it scored in each of 15 matches.

Goals scored	0	1	2	3
Frequency	3	6	4	2

Calculate the mean number of goals scored per match, giving your answer correct to 2 decimal places.

(Total for Question 8 is 2 marks)

The number of items bought by 20 customers at a market stall is shown below.

Items bought	1	2	3	4
Frequency	6	9	4	1

Write down (i) the modal number of items bought, and (ii) the total number of customers.

(Total for Question 9 is 2 marks)

The amount spent, in pounds, by 8 customers at a bakery stall is shown below.

Amount spent (GBP)	2	3	5
Frequency	3	4	1

Calculate the mean amount spent, giving your answer correct to 2 decimal places.

(Total for Question 10 is 2 marks)

A shoe shop records the sizes of 40 pairs of trainers sold in a week, to help decide which sizes to reorder.

Shoe size	4	5	6	7	8
Frequency	2	8	18	9	3

Which average (mode, median or mean) would be most useful to the manager when deciding which size to order more of? Give a reason for your answer.

(Total for Question 11 is 2 marks)

State whether this is True or False: For a frequency table with n data values, the position of the median is found using (n+1) divided by 2.

(Total for Question 12 is 1 mark)

The ages, in years, of pupils in a small tutor group are shown below.

Age	9	10	11
Frequency	2	5	1

Write down the age that has a frequency of 5.

(Total for Question 13 is 1 mark)

The number of books borrowed from a library by each of a group of members is shown below. One frequency is unknown, shown as x. The mean number of books borrowed is 2.5.

Books borrowed	1	2	3	4
Frequency	3	5	x	2

Work out the value of x.

(Total for Question 14 is 2 marks)

A cafe recorded the number of cakes bought by 25 customers one afternoon.

Cakes bought	0	1	2	3	4
Frequency	3	8	9	4	1

Calculate the mean number of cakes bought per customer, giving your answer correct to 2 decimal places.

(Total for Question 15 is 3 marks)

The number of visits made to a library in one month by 9 people is shown below. One person visited an unusually large number of times.

Visits	1	2	3	15
Frequency	4	3	1	1

(a)Calculate the mean number of visits, giving your answer correct to 1 decimal place.(2)

(b)One person visited 15 times, far more than anyone else. Explain which average, the mean or the median, better represents a typical person's number of visits.(1)

(Total for Question 16 is 3 marks)

A charity shop records the number of items bought by 20 customers in one morning.

Items bought	1	2	3	4	5
Frequency	2	5	7	4	2

Calculate the mean number of items bought per customer. The shop claims that, on average, customers buy at least 3 items. Does the mean support this claim? Give a reason.

(Total for Question 17 is 3 marks)

A call centre records the number of calls answered per hour by staff on two shifts, Morning and Evening, each covering 20 staff-hours.

Morning

Calls per hour	4	5	6	7
Frequency	2	5	8	5

Evening

Calls per hour	4	5	6	7
Frequency	3	4	6	7

(a)Calculate the mean calls per hour for the Morning shift.(1)

(b)Calculate the mean calls per hour for the Evening shift.(1)

(c)State which shift had the higher mean, and by how much.(1)

(Total for Question 18 is 3 marks)

60 members of a leisure centre were asked how many swimming sessions they attended last month. Two frequencies are unknown, shown as a and b. The mean number of sessions attended is 3.

Sessions	1	2	3	4	5
Frequency	10	a	18	b	4

Work out the values of a and b.

(Total for Question 19 is 3 marks)

A cafe till shows the number of coffees bought by 16 customers in an hour. One customer bought an unusually large number of coffees for a work meeting.

Coffees bought	1	2	3	10
Frequency	6	7	2	1

(a)Write down the median number of coffees bought.(1)

(b)Calculate the mean number of coffees bought, and explain why it is higher than the median.(2)

(Total for Question 20 is 3 marks)

Mark scheme · S03D Averages from a Frequency Table: Fluency and Exam Drill

Question 1

B1 1 cao
Answer: 1

Question 2

B1 14 cao
Answer: 14

Question 3

B1 True cao
Answer: True

Question 4

B1 B cao
Answer: B) sum(f times x) divided by sum(f)

Question 5

M1 identifies the median position as half(11+1) = 6th value, using cumulative frequencies 3, 8, 11
A1 6 cao
Answer: 6

Question 6

M1 identifies the median position as half(12+1) = 6.5th value (mean of 6th and 7th values), using cumulative frequencies 4, 9, 11, 12
A1 1 cao
Answer: 1

Question 7

M1 0x2+1x3+2x4+3x1 (=14), oe
A1 1.4 cao
Answer: 1.4

Question 8

M1 0x3+1x6+2x4+3x2 (=20), oe
A1 1.33 awrt
Answer: 1.33

Question 9

B1 (i) 2 cao
B1 (ii) 20 cao
Answer: (i) 2 (ii) 20

Question 10

M1 2x3+3x4+5x1 (=23), oe
A1 2.88 awrt
Answer: GBP 2.88

Question 11

B1 identifies the mode as the most useful average for this purpose
B1 valid justification, e.g. the mode shows the size that sold the most (size 6, frequency 18), so it tells the manager which size to reorder more of; the mean or median might not match a real, whole shoe size that needs restocking
Answer: Mode

Question 12

B1 True cao
Answer: True

Question 13

B1 10 cao
Answer: 10

Question 14

M1 sets up the mean equation (1x3+2x5+3x+4x2) divided by (3+5+x+2) = 2.5, oe, i.e. (21+3x) divided by (10+x) = 2.5
A1 x = 8 cao
Answer: x = 8

Question 15

M1 0x3+1x8+2x9+3x4+4x1 (=42), oe
M1 42 divided by 25
A1 1.68 cao
Answer: 1.68

Question 16

(a) M1 1x4+2x3+3x1+15x1 (=28), oe
(a) A1 3.1 awrt
(a) Answer: 3.1
(b) B1 median, because the single outlier of 15 visits pulls the mean up, whereas the median is not affected by it, oe
(b) Answer: Median, because it is not affected by the outlier of 15 visits, unlike the mean.

Question 17

M1 1x2+2x5+3x7+4x4+5x2 (=59), oe
A1 2.95 cao
B1 No, because 2.95 is less than 3, oe
Answer: Mean = 2.95. No, the claim is not supported, since 2.95 is less than the claimed 3 items.

Question 18

(a) B1 5.8 cao
(a) Answer: 5.8
(b) B1 5.85 cao
(b) Answer: 5.85
(c) B1 Evening, by 0.05 cao (ft from a and b)
(c) Answer: Evening, by 0.05 calls per hour.

Question 19

M1 total frequency equation: 10+a+18+b+4 = 60, i.e. a+b = 28, oe
M1 uses the mean to form 1x10+2a+3x18+4b+5x4 = 3x60, i.e. a+2b = 48, oe, and solves simultaneously with a+b=28
A1 a = 8 and b = 20, both cao
Answer: a = 8, b = 20

Question 20

(a) B1 2 cao
(a) Answer: 2
(b) B1 2.25 cao
(b) B1 explains that the customer who bought 10 coffees is an outlier that increases the mean but does not affect the median, oe
(b) Answer: Mean = 2.25. It is higher than the median because the one customer who bought 10 coffees is an outlier that pulls the mean up, but does not change the median.

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

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S03D Averages from a Frequency Table: Fluency and Exam Drill

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