Bar Charts: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

10 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics

2.15DB Bar Charts: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A charity shop's bar chart shows the number of items donated in one week: Books 34, Toys 19, Clothes 47, DVDs 8. Write down the number of toys donated.

(Total for Question 1 is 1 mark)

A school canteen's bar chart shows the number of lunch portions served: Pasta 36, Rice 24, Jacket potato 18, Salad 12. How many more portions of pasta were served than rice?

(Total for Question 2 is 1 mark)

A park ranger's bar chart shows how 220 visitors spent their time over a bank holiday weekend: Walking 85, Cycling 40, Other 15, and the rest were Picnicking. Work out the number of visitors who were picnicking.

(Total for Question 3 is 2 marks)

The bar chart below shows the rainfall (in mm) recorded at a weather station on each day last week. (a) Use the bar chart to write down the rainfall recorded on Wednesday. (b) Work out the range of the rainfall over the five days.

Figure (to be drawn): A bar chart titled 'Rainfall last week (mm)'. The vertical axis is labelled 'Rainfall (mm)' and is scaled from 0 to 30 in steps of 5, with a gridline at every step. The horizontal axis lists the days Monday to Friday, one bar per day. Bar heights: Monday 10, Tuesday 25, Wednesday 5, Thursday 15, Friday 20.

(a)Use the bar chart to write down the rainfall recorded on Wednesday.(1)

(b)Work out the range of the rainfall over the five days.(2)

(Total for Question 4 is 3 marks)

A cinema's bar chart shows the number of tickets sold for a film: Friday 240, Saturday 300. Calculate the percentage increase in tickets sold from Friday to Saturday.

(Total for Question 5 is 3 marks)

A charity park run's bar chart shows the number of runners in four age categories on Saturday: Under 18: 22, 18-40: 68, 41-60: 45, Over 60: 15. Show that the total number of runners was 150, and that the mean number of runners per age category was 37.5.

(Total for Question 6 is 4 marks)

Ayesha, a member of a hockey team, used the bar chart of goals scored in each of the team's 6 matches this season (2, 5, 1, 4, 3, 5) to find the mean. Her working was: 'Total = 2 + 5 + 1 + 4 + 3 + 5 = 20. Mean = 20 / 5 = 4.' (a) Show that Ayesha's total of 20 is correct, and explain why her mean of 4 is wrong. (b) Work out the correct mean number of goals per match, giving your answer correct to 1 decimal place.

(a)Show that Ayesha's total of 20 is correct, and explain why her mean of 4 is wrong.(2)

(b)Work out the correct mean number of goals per match, giving your answer correct to 1 decimal place.(2)

(Total for Question 7 is 4 marks)

A survey of 80 students at a college shows their favourite type of music: Pop 32, Rock 20, Hip-hop 16, Classical 12. (a) Work out the ratio of students who chose Rock to students who chose Classical, giving your answer in its simplest form. (b) The college has 960 students in total. Assuming the survey is representative of the whole college, estimate how many of all 960 students would choose Hip-hop as their favourite type of music.

(a)Work out the ratio of students who chose Rock to students who chose Classical, giving your answer in its simplest form.(2)

(b)The college has 960 students in total. Assuming the survey is representative of the whole college, estimate how many of all 960 students would choose Hip-hop as their favourite type of music.(4)

(Total for Question 8 is 6 marks)

A garden centre's bar chart compares the number of rose bushes sold in Spring and Summer across four types: Climbing (Spring 18, Summer 27), Shrub (Spring 34, Summer 40), Standard (Spring 12, Summer 15), Miniature (Spring 26, Summer 30). (a) Work out the total number of rose bushes sold in Spring. (b) Work out the percentage increase in total rose bush sales from Spring to Summer. Give your answer correct to 1 decimal place. (c) State which type of rose bush had the greatest percentage increase in sales from Spring to Summer. You must show your working.

(a)Work out the total number of rose bushes sold in Spring.(2)

(b)Work out the percentage increase in total rose bush sales from Spring to Summer. Give your answer correct to 1 decimal place.(4)

(c)State which type of rose bush had the greatest percentage increase in sales from Spring to Summer. You must show your working.(2)

(Total for Question 9 is 8 marks)

A running club recorded the time, t minutes, taken by 60 members to complete a 5 km run, grouped as follows: 20 ≤ t < 25: 8 members, 25 ≤ t < 30: 22 members, 30 ≤ t < 35: 19 members, 35 ≤ t < 40: 11 members. (a) Write down the modal class. (b) Use the midpoint of each class to estimate the mean time taken, giving your answer correct to 1 decimal place. (c) Comment on whether using the midpoints is likely to give an accurate estimate of the mean, given that a runner's finishing time is unlikely to be spread evenly across each 5-minute interval.

(a)Write down the modal class.(2)

(b)Use the midpoint of each class to estimate the mean time taken, giving your answer correct to 1 decimal place.(5)

(c)Comment on whether using the midpoints is likely to give an accurate estimate of the mean, given that a runner's finishing time is unlikely to be spread evenly across each 5-minute interval.(2)

(Total for Question 10 is 9 marks)

Mark scheme · 2.15DB Bar Charts: Fluency and Exam Drill (Part 2)

Question 1

B1 19 cao
Answer: 19

Question 2

B1 12 cao
Answer: 12 (36 - 24 = 12).

Question 3

M1 220 - (85 + 40 + 15) or equivalent method
A1 80 cao
Answer: 80 (220 - 140 = 80).

Question 4

(a) B1 5 mm cao
(a) Answer: 5 mm
(b) M1 identify the highest (25) and lowest (5) values, 25 - 5
(b) A1 20 mm cao
(b) Answer: 20 mm (25 - 5 = 20).

Question 5

M1 find the increase, 300 - 240 = 60
M1 60 / 240 x 100 oe
A1 25% cao
Answer: 25% (Increase = 60. 60 / 240 x 100 = 25%.)

Question 6

M1 add the four frequencies, 22 + 68 + 45 + 15
A1 = 150 shown correctly (cso)
M1 divide the total by the number of categories, 150 / 4
A1 = 37.5 shown correctly (cso), confirming both given values
Answer: Total = 150; mean = 37.5 runners per category (150 / 4 = 37.5).

Question 7

(a) M1 confirm 2 + 5 + 1 + 4 + 3 + 5 = 20
(a) A1 state Ayesha divided by 5 instead of 6 (there are 6 matches), which is why her mean is wrong
(a) Answer: Total = 20 is correct, but Ayesha divided by 5 instead of 6 (there are 6 matches), so her mean is wrong.
(b) M1 20 / 6
(b) A1 3.3 awrt
(b) Answer: 3.3 (20 / 6 = 3.333... = 3.3 to 1 dp).

Question 8

(a) M1 form the ratio 20 : 12
(a) A1 5 : 3 cao
(a) Answer: 5 : 3 (20 : 12 simplifies to 5 : 3).
(b) M1 form proportion 16/80 oe
(b) M1 multiply by 960, 960 x 16/80 oe
(b) A1 192 cao
(b) C1 state the assumption that the survey sample is representative of (has the same proportions as) the whole college
(b) Answer: 192 students (960 x 16/80 = 192).

Question 9

(a) M1 18 + 34 + 12 + 26
(a) A1 90 cao
(a) Answer: 90 (18 + 34 + 12 + 26 = 90).
(b) M1 total Summer sales, 27 + 40 + 15 + 30 = 112
(b) M1 find the increase, 112 - 90 = 22
(b) M1 22 / 90 x 100 oe
(b) A1 24.4% awrt
(b) Answer: 24.4% (Summer total = 112. Increase = 22. 22 / 90 x 100 = 24.444... = 24.4% to 1 dp.)
(c) M1 work out at least two of the percentage increases, e.g. Climbing (27-18)/18 x 100 = 50%, Standard (15-12)/12 x 100 = 25%
(c) A1 Climbing, 50% cao ft
(c) Answer: Climbing (an increase of 50%, compared with Shrub 17.6%, Standard 25% and Miniature 15.4%).

Question 10

(a) M1 identify the class with the highest frequency (22)
(a) A1 25 ≤ t < 30 cao
(a) Answer: 25 ≤ t < 30 (22 members, the highest frequency).
(b) M1 use midpoints 22.5, 27.5, 32.5, 37.5
(b) M1 multiply each midpoint by its frequency, e.g. 8 x 22.5, 22 x 27.5, 19 x 32.5, 11 x 37.5
(b) M1 sum the products, 180 + 605 + 617.5 + 412.5 = 1815
(b) M1 divide by the total frequency, 1815 / 60
(b) A1 30.3 awrt
(b) Answer: 30.3 minutes (1815 / 60 = 30.25, which rounds to 30.3 to 1 dp).
(c) M1 state that using midpoints assumes the times are evenly spread within each class, which may not be true
(c) A1 conclude it is only an estimate and could be an over- or underestimate of the true mean depending on how the times are actually distributed within each class
(c) Answer: It is only an estimate, not the exact mean: the midpoint method assumes times are evenly spread within each class, which may not be true, so the estimate could be higher or lower than the true mean.

Question 1

1 mark

Your answer

Question 2

1 mark

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Question 3

2 marks

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