Frequency Tables and Tally Charts - Worksheets, Questions and Revision

17 original exam-style questions - 11 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 12)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Statistics

S14 Frequency Tables and Tally Charts

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

For each statement about frequency tables and tally charts, write down whether it is True or False.

(i)A tally chart is a way of recording data by making a mark for each item as it is collected.(1)

(ii)In a tally chart, marks are grouped in fives, with the fifth mark drawn as a diagonal line crossing the first four.(1)

(iii)A frequency table displays every individual tally mark, rather than the total count for each category.(1)

(Total for Question 1 is 3 marks)

Each part shows a tally for one category. Work out the frequency it represents.

(a)Tally: ||||| ||(1)

(b)Tally: ||||| ||||| |||(1)

(c)Tally: ||||| ||||| |||||(1)

(Total for Question 2 is 3 marks)

The table shows the number of pupils in a class who chose each pet as their favourite.

Pet	Frequency
Dog	6
Cat	6
Fish	3
Bird	2

(a)Write down the mode or modes of favourite pet.(1)

(b)Work out the total number of pupils in the class.(2)

(Total for Question 3 is 3 marks)

Customers at a cafe were asked which drink they bought this morning. The table shows the results.

Drink	Frequency
Tea	11
Coffee	9
Juice	5
Water	3

(a)Work out the total number of customers surveyed.(2)

(b)Write down the mode.(1)

(c)Work out how many more customers chose tea than chose water.(1)

(Total for Question 4 is 4 marks)

24 pupils were asked how many pets they own. The tally chart shows the results, but the frequency column is incomplete.

Number of pets	Tally	Frequency
0	\|\|\|\|	?
1	\|\|\|\|\| \|\|\|	?
2	\|\|\|\|\| \|\|\|\|\|	?
3	\|\|	?

(a)Complete the frequency column of the table.(2)

(b)Work out the total number of pupils in the survey.(2)

(Total for Question 5 is 4 marks)

Here are the shoe sizes of 20 pupils in a class, in the order they were recorded:

6, 5, 7, 6, 8, 5, 6, 9, 6, 7, 5, 6, 8, 7, 6, 5, 9, 6, 7, 5

(a)Complete a tally chart and frequency table for shoe sizes 5, 6, 7, 8 and 9, using the raw list above.(3)

(b)Write down the modal shoe size.(1)

(c)Work out the total number of pupils, and use it to check your frequency table is correct.(2)

(Total for Question 6 is 6 marks)

The times, in seconds, taken by 20 runners to complete a sprint are recorded below, in the order the runners finished:

14.1, 12.3, 16.4, 18.2, 15.6, 13.9, 19.8, 14.8, 17.5, 12.9, 15.0, 18.9, 16.7, 14.6, 13.4, 19.2, 17.1, 15.9, 18.4, 14.2

(a)Complete a grouped tally chart and frequency table for this data, using the class intervals 12-13.9, 14-15.9, 16-17.9 and 18-19.9 seconds.(3)

(b)Write down the modal class.(1)

(Total for Question 7 is 4 marks)

43 people at a cafe were asked whether they preferred tea or coffee. The two-way table shows some of the results; some entries are missing.

Group	Tea	Coffee	Total
Adults	15	?	25
Children	?	6	18
Total	?	?	43

(a)Work out the missing number of adults who preferred coffee.(1)

(b)Work out the missing number of children who preferred tea.(1)

(c)Work out the total number of people who preferred tea.(2)

(Total for Question 8 is 4 marks)

40 pupils were asked whether they preferred football or swimming. The two-way table shows the results, with some entries given as tally marks.

Group	Football	Swimming
Boys	\|\|\|\|\| \|\|\|\|\| \|\|	10
Girls	8	\|\|\|\|\| \|\|\|\|\|

(a)Convert the two tally entries in the table into frequencies.(2)

(b)Work out the total number of boys, and the total number of girls, who took part in the survey.(2)

(c)Use the row and column totals to work out the total number of pupils who preferred swimming.(2)

(Total for Question 9 is 6 marks)

The two-way table shows the favourite subject (Maths, English or Science) of pupils in Year 9 and Year 10.

Year group	Maths	English	Science	Total
Year 9	14	10	6	30
Year 10	9	15	11	35
Total	23	25	17	65

(a)Write down the total number of pupils surveyed.(1)

(b)Work out how many more Year 10 pupils chose English than chose Science.(2)

(c)A pupil says, 'More pupils overall chose Science than chose English.' Use the table to show that the pupil is wrong, and give the correct comparison.(2)

(Total for Question 10 is 5 marks)

A pupil records the number of pets owned by her class using a tally chart, then copies the frequencies into a table. The register shows that there are 26 pupils in the class, but she thinks she may have made a copying error somewhere.

Pets owned	Tally	Frequency (as she wrote it)
0	\|\|\|\|\| \|\|\|\|\|	8
1	\|\|\|\|\| \|\|\|	8
2	\|\|\|\|\|	5
3	\|\|\|	3

(a)Show that the frequencies she has written do not add up to the 26 pupils on the register.(2)

(b)Identify which row's frequency was copied incorrectly from the tally, and state the correct frequency for that row.(2)

(Total for Question 11 is 4 marks)

A student wants to investigate which lunch option is most popular among Year 8 pupils: a hot meal, a packed lunch, or a home lunch (going home to eat). This question follows her investigation through the stages of the statistical enquiry cycle.

(a)Plan: Design a suitable data collection sheet that the student could use to record each pupil's answer as she asks them, one at a time.(2)

(b)Collect: The student asks 24 pupils and notes down each answer as it is given:

Hot meal, Packed lunch, Hot meal, Home lunch, Packed lunch, Hot meal, Hot meal, Packed lunch, Home lunch, Hot meal, Packed lunch, Hot meal, Home lunch, Packed lunch, Hot meal, Packed lunch, Hot meal, Home lunch, Packed lunch, Hot meal, Packed lunch, Home lunch, Hot meal, Packed lunch

Complete the tally chart and frequency table for this data.(3)

(c)Process: Write down the mode of the pupils' lunch choices, and work out the total number of pupils who chose either a packed lunch or a home lunch.(3)

(d)Interpret: The student concludes, 'Most pupils bring a packed lunch.' Use your frequency table to say whether the student's conclusion is correct, and explain your reasoning.(2)

(Total for Question 12 is 10 marks)

A pupil is grouping data on the number of text messages sent by 24 pupils in a day. She chooses these class intervals for her tally chart: 0-10, 10-20, 20-30, 32-40.

(a)Give two reasons why these class intervals are not suitable for a grouped tally chart.(2)

(b)Suggest a suitable set of four class intervals to replace them, covering the range 0 to 40 with no overlaps or gaps.(2)

(Total for Question 13 is 4 marks)

36 pupils were asked whether they preferred cats or dogs as a pet. The two-way table shows the results.

Group	Cats	Dogs
Boys	7	11
Girls	13	5

(a)Write down, as a fraction, the proportion of all 36 pupils who were girls who preferred cats.(1)

(b)A pupil says, 'Exactly half of the 36 pupils preferred dogs.' Determine whether the pupil is correct, showing your working.(3)

(Total for Question 14 is 4 marks)

A researcher wants to find out how many hours per week local people spend exercising. She plans to stand outside a gym on a weekday morning and ask the first 30 people she sees to tally their answer into pre-set class intervals.

(a)Give two reasons why this sample might not be representative of 'local people' in general.(2)

(b)Suggest one improvement the researcher could make to her data collection method.(2)

(Total for Question 15 is 4 marks)

The grouped frequency table shows the waiting times, in minutes, of 30 people at a bus stop.

Waiting time (minutes)	Frequency
0-4	6
5-9	11
10-14	8
15-19	5

(a)Write down the modal class.(1)

(b)A newspaper report claims, 'More than half of all the people waited under 10 minutes.' Determine, showing your working, whether this claim is correct.(3)

(c)Work out the total number of people who waited 10 minutes or more.(2)

(Total for Question 16 is 6 marks)

A student is collecting data on the colour of 200 cars passing a junction, one at a time, over the course of an hour. Explain why using a tally chart to record each car's colour as it passes is more efficient than writing a full list of colours and counting them up at the end.

(Total for Question 17 is 2 marks)

Mark scheme · S14 Frequency Tables and Tally Charts

Question 1

(i) B1 True cao
(i) Answer: True
(ii) B1 True cao
(ii) Answer: True
(iii) B1 False cao
(iii) Answer: False

Question 2

(a) B1 7 cao
(a) Answer: 7
(b) B1 13 cao
(b) Answer: 13
(c) B1 15 cao
(c) Answer: 15

Question 3

(a) B1 Dog and Cat cao (bimodal)
(a) Answer: Dog and Cat
(b) M1 6 + 6 + 3 + 2, oe
(b) A1 17 cao
(b) Answer: 17

Question 4

(a) M1 11 + 9 + 5 + 3, oe
(a) A1 28 cao
(a) Answer: 28
(b) B1 Tea cao
(b) Answer: Tea
(c) B1 8 cao
(c) Answer: 8

Question 5

(a) B2 all four frequencies correct: 4, 8, 10, 2
(a) Answer: 0 pets: 4, 1 pet: 8, 2 pets: 10, 3 pets: 2
(b) M1 4 + 8 + 10 + 2, oe ft their frequencies
(b) A1 24 cao ft
(b) Answer: 24

Question 6

(a) B2 all five frequencies correct: 5, 7, 4, 2, 2 (for sizes 5, 6, 7, 8, 9)
(a) B1 tally marks correctly grouped in fives throughout
(a) Answer: Size 5: 5, Size 6: 7, Size 7: 4, Size 8: 2, Size 9: 2
(b) B1 6 cao ft
(b) Answer: 6
(c) M1 5 + 7 + 4 + 2 + 2, oe ft their frequencies
(c) A1 20 cao ft, matching the 20 pupils in the list
(c) Answer: 20

Question 7

(a) B2 all four frequencies correct: 4, 7, 4, 5
(a) B1 every time tallied into exactly one class, with no overlaps or gaps between the given intervals
(a) Answer: 12-13.9: 4, 14-15.9: 7, 16-17.9: 4, 18-19.9: 5
(b) B1 14-15.9 cao ft
(b) Answer: 14-15.9 seconds

Question 8

(a) B1 10 cao
(a) Answer: 10
(b) B1 12 cao
(b) Answer: 12
(c) M1 15 + 12, oe ft
(c) A1 27 cao ft
(c) Answer: 27

Question 9

(a) B1 Boys-Football: 12 cao
(a) B1 Girls-Swimming: 10 cao
(a) Answer: Boys-Football = 12, Girls-Swimming = 10
(b) M1 12 + 10 and 8 + 10, oe ft
(b) A1 Boys = 22 and Girls = 18, cao ft
(b) Answer: Boys = 22, Girls = 18
(c) M1 10 + 10, oe ft (Boys-Swimming + Girls-Swimming)
(c) A1 20 cao ft
(c) Answer: 20

Question 10

(a) B1 65 cao
(a) Answer: 65
(b) M1 15 - 11, oe
(b) A1 4 cao
(b) Answer: 4
(c) M1 identifies the column totals: Science = 17 and English = 25, oe
(c) A1 correct conclusion: English (25) is greater than Science (17), so the pupil is wrong
(c) Answer: The pupil is wrong: 25 pupils chose English compared with 17 who chose Science.

Question 11

(a) M1 8 + 8 + 5 + 3, oe
(a) A1 24, which is not equal to 26
(a) Answer: 24 (not 26)
(b) B1 0 pets row identified
(b) B1 10 cao
(b) Answer: 0 pets: should be 10, not 8

Question 12

(a) B1 three appropriate, non-overlapping categories listed matching the context (hot meal, packed lunch, home lunch)
(a) B1 a tally column and a frequency column included, both correctly labelled
(a) Answer: A table with columns 'Lunch option', 'Tally' and 'Frequency', with the three categories listed as rows.
(b) B2 all three frequencies correct: Hot meal = 10, Packed lunch = 9, Home lunch = 5
(b) B1 tally marks correctly grouped in fives
(b) Answer: Hot meal: 10, Packed lunch: 9, Home lunch: 5
(c) B1 Hot meal cao ft
(c) M1 9 + 5, oe ft
(c) A1 14 cao ft
(c) Answer: Mode: Hot meal; packed lunch or home lunch: 14
(d) M1 compares the mode (Hot meal, 10) with Packed lunch (9), oe ft
(d) A1 concludes the student is incorrect, since Hot meal (10) was chosen by more pupils than Packed lunch (9), ft
(d) Answer: The student is incorrect: Hot meal (10 pupils) was more popular than Packed lunch (9 pupils).

Question 13

(a) B1 0-10 and 10-20 overlap, so a value of exactly 10 could be tallied into either class
(a) B1 there is a gap between 30 and 32, so a value of 31 would not fit into any class
(a) Answer: The intervals overlap at 10, and there is a gap between 30 and 32.
(b) B2 a correct set of four equal-width, non-overlapping, gap-free intervals covering 0-40, e.g. 0-9, 10-19, 20-29, 30-39 (accept equivalent notation)
(b) Answer: 0-9, 10-19, 20-29, 30-39

Question 14

(a) B1 13/36 oe
(a) Answer: 13/36
(b) M1 11 + 5 (=16), oe
(b) A1 16/36, which simplifies to 4/9
(b) A1 the pupil is incorrect, since 4/9 is not equal to 1/2 (18/36), dep on both previous marks
(b) Answer: Incorrect: 16 out of 36 pupils (4/9) preferred dogs, not half (18/36).

Question 15

(a) B1 standing outside a gym oversamples people who already exercise regularly, compared with the wider local population
(a) B1 a weekday morning misses people who are at work or school at that time, so the sample is biased towards those who are free then
(a) Answer: The location oversamples regular exercisers, and the timing misses people who work weekday mornings.
(b) B2 a valid, justified improvement, e.g. selecting people at random from several different locations and at different times of day/week, not only outside a gym on one weekday morning
(b) Answer: Sample people at random from a range of locations and times, not only outside a gym on a weekday morning.

Question 16

(a) B1 5-9 cao
(a) Answer: 5-9 minutes
(b) M1 6 + 11 (=17), oe
(b) A1 17/30
(b) A1 the claim is correct, since 17/30 is greater than 1/2 (15/30), dep on both previous marks
(b) Answer: Correct: 17 out of 30 people (more than half) waited under 10 minutes.
(c) M1 8 + 5, oe
(c) A1 13 cao
(c) Answer: 13