Comparing Data Sets - Worksheets, Questions and Revision

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GCSE · Statistics

S08 Comparing Data Sets

EDEXCEL 1ST0 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Two swimming clubs each timed their members over 50m. The table shows summary statistics for their times.
Mean time (s)Range (s)
Club A34.25.1
Club B35.68.7
(a)Compare the mean swim times of Club A and Club B.(1)
(b)Compare the ranges of the two clubs.(1)
(c)Using both the mean and the range, write a conclusion comparing the two swimming clubs.(2)
(Total for Question 1 is 4 marks)
2
The bar charts show the number of each drink sold at two cafes one morning.
(a)From the bar chart for Cafe A, write down the modal (most popular) drink.(1)
0 2 4 6 8 10 12 14 16 18 20 Tea Coffee Juice Water Drink (Cafe A) Number sold
(b)From the bar chart for Cafe B, write down the modal (most popular) drink.(1)
0 2 4 6 8 10 12 14 16 18 20 Tea Coffee Juice Water Drink (Cafe B) Number sold
(c)Compare the two cafes' most popular drinks, and suggest one reason why they might differ.(2)
(Total for Question 2 is 4 marks)
3
For each statement about comparing data sets, write down whether it is True or False.
(i)The range only uses the smallest and largest values in a data set.(1)
(ii)The mean is always the best average to use when comparing two data sets.(1)
(iii)Two data sets can have the same mean but different ranges.(1)
(Total for Question 3 is 3 marks)
4
The daily temperatures (in degrees Celsius) were recorded for two towns over 6 days.

Elm: 14, 16, 15, 13, 17, 15

Oak: 18, 9, 20, 8, 17, 6
(a)Calculate the mean temperature for Elm.(2)
(b)Calculate the mean temperature for Oak.(2)
(c)Calculate the range of temperatures for each town.(2)
(d)Compare the two towns' weather using your answers, and write a conclusion.(1)
(Total for Question 4 is 7 marks)
5
Class A has 8 students; the range of their test scores is 45 marks. Class B has 32 students; the range of their test scores is 20 marks. A student claims: "Class A's test scores are more spread out than Class B's, because Class A has the bigger range."
(a)Explain one reason why comparing the ranges of Class A (8 students) and Class B (32 students) directly might be misleading.(1)
(b)Suggest a more appropriate statistic to compare the spread of the two classes' scores, and explain why it would give a fairer comparison.(2)
(Total for Question 5 is 3 marks)
6
A call centre records the number of calls answered per hour by staff on two different shifts.
Calls per hour34567
Frequency (Shift A)25841
Frequency (Shift B)13673
(a)Find the median number of calls answered per hour for Shift A. (There are 20 staff-hours recorded for Shift A.)(2)
(b)Find the median number of calls answered per hour for Shift B. (There are 20 staff-hours recorded for Shift B.)(2)
(c)Compare the two shifts using the medians, and write a conclusion in context.(2)
(Total for Question 6 is 6 marks)
7
Two small companies each employ 5 staff. Their annual salaries are shown below.

Company A: £22000, £23000, £24000, £25000, £26000

Company B: £20000, £21000, £22000, £23000, £95000 (the owner's salary)
(a)Calculate the mean salary for each company.(2)
(b)Calculate the median salary for each company.(2)
(c)Explain why the median is a more appropriate measure than the mean to compare typical salaries at the two companies, referring to your answers.(2)
(Total for Question 7 is 6 marks)
8
Two schools recorded how long (in minutes) their Year 10 students spent on homework one evening.

School P
Time, t (minutes)0≤t<2020≤t<4040≤t<6060≤t<8080≤t<100
Frequency4101484

School Q
Time, t (minutes)0≤t<2020≤t<4040≤t<6060≤t<8080≤t<100
Frequency8141053
(a)Calculate an estimate of the mean homework time for School P.(3)
(b)Calculate an estimate of the mean homework time for School Q.(3)
(c)Compare the two schools' typical homework times.(1)
(Total for Question 8 is 7 marks)
9
Two groups of volunteers each timed how many minutes it took them to solve the same puzzle. The times, in order, were:

Group P (9 people): 8, 10, 11, 12, 12, 13, 14, 15, 19

Group Q (9 people): 9, 9, 10, 10, 11, 12, 15, 17, 21
(a)For Group P, find the lower quartile, the upper quartile and the interquartile range.(3)
(b)For Group Q, find the lower quartile, the upper quartile and the interquartile range.(3)
(c)Compare the consistency of the two groups using the interquartile range, and write a conclusion.(2)
(Total for Question 9 is 8 marks)
10
The box plots show the number of hours per week that Year 10 and Year 11 students spent on homework, based on a survey at a school.
0 2 4 6 8 10 12 14 16 18 20 Hours spent on homework per week Year 10 Year 11
(a)Write down the median number of hours spent on homework per week for each year group.(2)
(b)Find the interquartile range for each year group.(2)
(c)Compare the two year groups using the median and the interquartile range, and write a conclusion.(2)
(Total for Question 10 is 6 marks)
11
A student is comparing commute times for two routes to college.
(a)On the grid, draw a box plot for the Bus route using this five-number summary: minimum 5 minutes, lower quartile 12 minutes, median 18 minutes, upper quartile 24 minutes, maximum 29 minutes.(3)
0 5 10 15 20 25 30 Bus commute time (minutes)
(b)The box plot for the Train route is shown. Find the interquartile range for the Train route.(2)
0 5 10 15 20 25 30 Train commute time (minutes)
(c)Compare the two routes' commute times using the median and the interquartile range, and suggest which route would give a more reliable journey time.(2)
(Total for Question 11 is 7 marks)
12
A student is investigating whether reaction times differ between two age groups at a science fair: Under 16s and Adults. Raw reaction times (in milliseconds) collected from a sample of each group were:

Under 16s: 210, 225, 198, 240, 215, 205

Adults: 180, 175, 190, 185, 170, 300
(a)Suggest a suitable method the student could use to select a sample of participants for each age group, and give one reason why this method would help make a fair comparison.(2)
(b)Calculate the mean and the range of the reaction times for each age group, using all the data given.(4)
(c)One adult recorded a reaction time of 300 ms, much higher than the rest of that group. State what this value is called, and recalculate the mean and the range for the Adults group with this value removed.(3)
(d)Using the most appropriate statistics, write a conclusion comparing the reaction times of the two age groups.(2)
(Total for Question 12 is 11 marks)
13
For each statement about comparing data sets, write down whether it is True or False.
(i)If two data sets have the same range, they must have the same spread for most of their values.(1)
(ii)The interquartile range ignores extreme outliers, so it can give a fairer picture of consistency than the range.(1)
(iii)You can compare the averages of two data sets by comparing their medians, even if one data set has an outlier.(1)
(iv)A larger sample size always makes a data set more consistent.(1)
(Total for Question 13 is 4 marks)
14
Two garages, X and Y, each recorded the time taken (in minutes) to service 60 cars. The cumulative frequency graphs for both garages are shown on the same axes.
0 10 20 30 40 50 60 0 10 20 30 40 50 Service time (minutes) Cumulative frequency Garage X (solid line) Garage Y (dashed line)
(a)Use the graphs to find the median service time for each garage.(2)
(b)Use the graphs to find the interquartile range for each garage.(4)
(c)Compare the two garages, using your answers to parts (a) and (b).(2)
(Total for Question 14 is 8 marks)
15
Two factories recorded the number of defective items produced over a 7-day week.

Factory M: 2, 3, 3, 4, 3, 25, 3

Factory N: 5, 6, 7, 8, 9, 10, 11

A trainee says: "Factory M's output is more variable than Factory N's, because Factory M has the larger range (23 defects compared with 6 defects)."
(a)Calculate the interquartile range for each factory.(2)
(b)Comment on whether the trainee's claim is fair, using your answers to part (a).(2)
(Total for Question 15 is 4 marks)
16
A quality inspector at a drinks factory samples 4 bottles from each of two filling machines and measures the volume (in ml).

Machine A: 496, 498, 502, 504

Machine B: 480, 500, 500, 520
(a)Show that the mean volume is 500 ml for both Machine A and Machine B.(1)
(b)Calculate the standard deviation of Machine A's volumes.(3)
(c)Calculate the standard deviation of Machine B's volumes.(3)
(d)Compare the two machines using the standard deviations calculated, and state which machine fills bottles more reliably.(2)
(Total for Question 16 is 9 marks)
17
Three sprinters' 100m race times over a season are summarised below.
RunnerMean (s)Median (s)Range (s)IQR (s)Standard deviation (s)
Amara12.112.01.80.90.31
Beth12.412.30.60.50.18
Cara12.612.52.41.60.52
(a)Which runner has the fastest average 100m time? Justify your answer using the table.(2)
(b)Which runner is the most consistent? Justify your answer using the table.(2)
(c)A coach says: "Beth is the best runner because she has the smallest range." Comment on this statement, referring to the other statistics in the table.(2)
(Total for Question 17 is 6 marks)
Mark scheme · S08 Comparing Data Sets

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

Question 17