Frequency Polygons - Worksheets, Questions and Revision

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GCSE · Statistics

S27 Frequency Polygons

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
20 people were surveyed about how long, in minutes, their last phone call lasted. The frequency polygon shows the results.
024681005101520Length of phone call (minutes)Frequency
(a)Write down the frequency of calls lasting more than 5 minutes but no more than 10 minutes.(1)
(b)Work out the total number of people represented by the frequency polygon.(2)
(Total for Question 1 is 3 marks)
2
A frequency polygon is most appropriate for displaying which type of data?
  • A) Categorical data, such as favourite colour
  • B) Continuous grouped data, such as height recorded in class intervals
  • C) Qualitative data with no numerical value
  • D) Two unrelated categorical variables shown together
(Total for Question 2 is 1 mark)
3
For each statement about frequency polygons, write down whether it is True or False.
(i)The height of each plotted point on a frequency polygon represents a frequency.(1)
(ii)A frequency polygon plots frequency against the upper class boundary of each interval.(1)
(iii)Two frequency polygons can be drawn on the same axes to compare two distributions.(1)
(iv)The modal class of a distribution shown by a frequency polygon is the class at the lowest plotted point.(1)
(Total for Question 3 is 4 marks)
4
40 people completed a jigsaw puzzle at a puzzle cafe. The time taken, in minutes, is shown in the frequency polygon below.
024681012141601020304050Time taken (minutes)Frequency
(a)Write down the frequency of the class 10 < t ≤ 20.(1)
(b)Write down the modal class.(1)
(c)Work out the number of people who took more than 30 minutes to complete the puzzle.(2)
(Total for Question 4 is 4 marks)
5
25 children were asked how much pocket money, in GBP, they receive each week. The frequency polygon shows the results.
02468100510152025Pocket money (GBP)Frequency
(a)Write down the modal class.(1)
(b)Work out how many children receive £15 or less pocket money each week.(2)
(Total for Question 5 is 3 marks)
6
The frequency polygon shows the speeds, in mph, of 38 cars recorded on a residential road with a 30 mph speed limit.
048121620202530354045Speed (mph)Frequency
(a)Which word best describes the skew of this distribution?(1)
  • A) Symmetrical
  • B) Positively skewed (skewed to the right)
  • C) Negatively skewed (skewed to the left)
  • D) Uniform (no skew)
(b)Give a reason for your answer, referring to the shape of the frequency polygon.(1)
(Total for Question 6 is 2 marks)
7
An airline checked in the luggage of 60 passengers at a check-in desk. The frequency polygon shows the weight, in kg, of each passenger's luggage.
04812162024102030405060Weight of luggage (kg)Frequency
(a)Write down the modal class.(1)
(b)Estimate the number of passengers whose luggage weighed more than 40 kg.(2)
(c)The airline charges an excess fee of £15 for each bag that weighs more than 40 kg. Work out an estimate for the total excess fees collected from these 60 passengers.(2)
(Total for Question 7 is 5 marks)
8
A print shop recorded the number of pages printed for each of 50 print jobs one day. The frequency polygon below shows the results, but the point for the class 40 < p ≤ 60 is missing.
024681012141618020406080100Number of pages printedFrequencyf = ?
(a)The total number of print jobs is 50. Work out the value of f, the frequency of the class 40 < p ≤ 60.(3)
(b)Write down the coordinates that should be plotted for this class.(1)
(Total for Question 8 is 4 marks)
9
30 employees at a company were asked how far, in km, they travel to work. The grouped frequency table shows the results.
Distance (km)Frequency
0 < d ≤ 45
4 < d ≤ 89
8 < d ≤ 128
12 < d ≤ 165
16 < d ≤ 203
Total30
012345678910048121620Distance travelled to work (km)Frequency
(a)Write down the midpoint of each class interval.(2)
(b)On the grid provided, draw the frequency polygon for this information.(3)
(Total for Question 9 is 5 marks)
10
60 teenagers were asked how many text messages they sent yesterday. The frequency polygon shows the results.
024681012141618202224020406080100Number of texts sentFrequency
(a)Write down the modal class.(1)
(b)Describe the shape of the distribution shown by the frequency polygon.(2)
(c)Estimate the number of teenagers who sent fewer than 40 texts.(2)
(Total for Question 10 is 5 marks)
11
Two garden centres, Garden A and Garden B, each measured the height, in cm, of a sample of 40 sunflower plants. The frequency polygons for both distributions are shown on the same axes.
0246810121416100120140160180200Height of sunflower plant (cm)FrequencyGarden AGarden B
(a)Write down the modal class for Garden A.(1)
(b)Write down the modal class for Garden B.(1)
(c)Compare the shapes of the two distributions. Use the word 'skewed' in your answer.(2)
(Total for Question 11 is 4 marks)
12
45 people attending a yoga class had their age, in years, recorded. The frequency polygon shows the results.
0246810121416203040506070Age (years)Frequency
(a)Using the frequency polygon, write down the number of people aged between 40 and 50.(1)
(b)One of the yoga teachers claims: "More than 20 people at the class were over the age of 50." Determine whether the teacher is correct. Show your working.(2)
(c)Estimate the percentage of people at the class who were aged under 40.(3)
(Total for Question 12 is 6 marks)
13
A researcher is investigating how long it takes people to commute to work. She plans to collect data from a sample of workers and present her results using a frequency polygon.
(a)Plan: Write a suitable question the researcher could use in a questionnaire to collect this data. Your question must produce numerical data.(1)
(b)Collect: The researcher considers asking only people arriving at one particular railway station. State one reason why this might not produce a sample representative of all commuters.(1)
(c)Process: The table shows the grouped commuting-time data she collected from 50 workers. Complete the midpoint column.
Commuting time (minutes)FrequencyMidpoint
0 < t ≤ 156
15 < t ≤ 3018
30 < t ≤ 4516
45 < t ≤ 607
60 < t ≤ 753
(2)
(d)Interpret: The frequency polygon for this data is shown below. Write down the modal class, and use it to describe what this tells you about the commuting times of most workers in the sample.(2)
0246810121416182001530456075Commuting time (minutes)Frequency
(Total for Question 13 is 6 marks)
14
A delivery depot recorded the weight, in kg, of 50 parcels processed one morning. The frequency polygon shows the results.
024681012141618048121620Weight of parcel (kg)Frequency
(a)Write down the frequency of the class 8 < w ≤ 12.(1)
(b)Estimate the number of parcels weighing more than 12 kg.(2)
(c)Use the frequency polygon to estimate the mean weight of the parcels.(3)
(Total for Question 14 is 6 marks)
15
40 pupils' times, in seconds, for a 100 m sprint on sports day are shown in the frequency polygon below.
024681012141618121314151617Time (seconds)Frequency
(a)Write down the modal class.(1)
(b)State, with a reason, whether the distribution is symmetrical.(2)
(c)When the 40 times are placed in order from fastest to slowest, the 20th and 21st times both lie in the class 14 < t ≤ 15. Use linear interpolation to estimate the median time.(3)
(Total for Question 15 is 6 marks)
16
Two mock exam papers were sat by the same class of 30 students. The frequency polygons show the marks, out of 80, for Paper 1 and Paper 2.
02468101201632486480Mark (out of 80)FrequencyPaper 1Paper 2
(a)Show that the estimated mean mark for Paper 1 is 44.8.(3)
(b)Calculate the estimated mean mark for Paper 2.(3)
(c)State, with a reason, which paper the class found more difficult.(2)
(Total for Question 16 is 8 marks)
Mark scheme · S27 Frequency Polygons

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