Frequency Polygons: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

8 original exam-style questions - 3 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 4)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Statistics

2.13DB Frequency Polygons: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A frequency table shows how long, in minutes, each customer waited in a queue at a post office in Cardiff.
Waiting time (minutes): 0-5, 5-10, 10-15, 15-20
Frequency: 6, 9, 7, 3
Write down the width of the class 10-15.

(Total for Question 1 is 1 mark)

A cycling club recorded the distances, in km, ridden by members last weekend.
Distance (km): 0-10, 10-25, 25-40, 40-60
Frequency: 5, 12, 9, 4
Find the midpoint of the class 10-25.

(Total for Question 2 is 1 mark)

A GP surgery in Leeds recorded the ages, in years, of patients attending a flu clinic in grouped classes.
Age (years): 0-20, 20-40, 40-60, 60-80
Frequency: 8, 15, x, 11
The total number of patients was 50. Calculate the value of x.

(Total for Question 3 is 2 marks)

A bakery recorded the number of loaves sold per day over several weeks, grouped into classes.
Loaves sold: 20-29, 30-39, 40-49, 50-59
Frequency: 5, 13, 9, 3
State the class with the lowest frequency.

(Total for Question 4 is 2 marks)

A garden centre recorded the heights, in cm, of tomato plants, grouped into classes.
Height (cm): 40-60, 60-80, 80-100, 100-120
Frequency: 4, 10, 14, 6
Estimate the range of the heights, using the boundaries of the classes.

(Total for Question 5 is 3 marks)

A theatre recorded how long, in minutes, it took each group of latecomers to reach their seats after a show had started.
Time (minutes): 0-5, 5-10, 10-20, 20-40
Frequency: 6, 10, 8, 2
Show that the estimated mean time is 10.4 minutes, to 1 decimal place.

(Total for Question 6 is 3 marks)

A student is estimating the mean number of emails received per day by staff at a small office, from this grouped frequency table.
Emails received: 0-9, 10-19, 20-29, 30-39
Frequency: 3, 7, 8, 2
The student's working is shown below.
Midpoints used: 9, 19, 29, 39
Sum of (midpoint x frequency) = (9 x 3) + (19 x 7) + (29 x 8) + (39 x 2) = 27 + 133 + 232 + 78 = 470
Estimated mean = 470 / 20 = 23.5

(a)Identify the error in the student's method.(1)

(b)Work out the correct estimate for the mean number of emails received per day.(3)

(Total for Question 7 is 4 marks)

The frequency polygons show the times, in minutes, taken by runners from Oakwood Running Club and Bridgeton Running Club to complete a 5 km parkrun.

Figure (to be drawn): Two frequency polygons plotted on the same axes. Horizontal axis 'Time (minutes)' labelled from 15 to 40 in steps of 5. Vertical axis 'Frequency' labelled from 0 to 16 in steps of 2. Oakwood Running Club plotted as a solid line through points at class midpoints (17.5, 4), (22.5, 12), (27.5, 14), (32.5, 6), (37.5, 2), each pair of consecutive points joined by a straight line segment. Bridgeton Running Club plotted as a dashed line through points at the same midpoints (17.5, 1), (22.5, 4), (27.5, 9), (32.5, 15), (37.5, 9), each pair of consecutive points joined by a straight line segment. A key identifies the solid line as Oakwood and the dashed line as Bridgeton. Caption: NOT accurately drawn.

(a)Using the frequency polygon, write down the number of Bridgeton Running Club runners who took between 25 and 30 minutes.(1)

(b)Compare the distributions of times for the two running clubs.(3)

(Total for Question 8 is 4 marks)

Mark scheme · 2.13DB Frequency Polygons: Fluency and Exam Drill (Part 2)

Question 1

B1 5 cao
Answer: 5

Question 2

B1 17.5 cao
Answer: 17.5

Question 3

M1 adds known frequencies 8 + 15 + 11 (= 34) oe, or 50 - 34 seen
A1 16 cao
Answer: 16

Question 4

M1 identifies the smallest frequency, 3
A1 50-59 cao
Answer: 50-59

Question 5

M1 identifies the upper boundary of the largest class as 120
M1 identifies the lower boundary of the smallest class as 40
A1 80 (cm) cao
Answer: 80 cm

Question 6

M1 uses midpoints 2.5, 7.5, 15, 30 oe
M1 forms sum of (midpoint x frequency) = 270 and divides by total frequency 26
A1 10.4 (minutes) cso, all working shown correctly
Answer: 10.4 minutes (shown)

Question 7

(a) B1 states that the student used the upper boundary of each class instead of the midpoint oe
(a) Answer: The student used the upper boundary of each class (9, 19, 29, 39) instead of the midpoint of each class.
(b) M1 uses correct midpoints 4.5, 14.5, 24.5, 34.5
(b) M1 forms sum of (midpoint x frequency) = 380 and divides by total frequency 20
(b) A1 19 cao
(b) Answer: 19

Question 8

(a) B1 9 cao
(a) Answer: 9
(b) M1 valid comparison of a typical/average time, e.g. Oakwood runners were generally faster than Bridgeton runners oe
(b) M1 valid comparison of spread or shape, e.g. Bridgeton's times are more spread towards the higher end / less consistent than Oakwood's oe
(b) A1 both comparisons correctly supported by a reference to the graph, e.g. correct modal classes quoted (Oakwood 25-30, Bridgeton 30-35) or correct direction of shift quoted
(b) Answer: On average, Oakwood runners were faster than Bridgeton runners (Oakwood's modal class is 25-30 minutes, Bridgeton's is 30-35 minutes). Bridgeton's times are more spread out towards the higher times, so Bridgeton's times were less consistent than Oakwood's.

Question 1

1 mark

Your answer

Question 2

1 mark

Your answer

Question 3

2 marks

Your answer

Question 4

2 marks

Your answer

Question 5

3 marks

Your answer

Question 6

3 marks

Your answer

Question 7

4 marks

Did your answer earn the marks?

Question 8

4 marks

Did your answer earn the marks?

Mark my answers

Frequency Polygons: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

More on this topic

Next in this strand

2.13DB Frequency Polygons: Fluency and Exam Drill (Part 2)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Mark your answers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8