Median Quartiles and IQR - Worksheets, Questions and Revision

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GCSE · Statistics

S12 Median Quartiles and IQR

EDEXCEL 1ST0 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
For each statement about the median, quartiles and interquartile range (IQR), write down whether it is True or False.
(i)The median is always one of the values in the original data set.(1)
(ii)The interquartile range is found by working out the upper quartile minus the lower quartile.(1)
(iii)Roughly half of the data values lie between the lower quartile and the upper quartile.(1)
(Total for Question 1 is 3 marks)
2
A student is deciding whether to use the range or the interquartile range (IQR) to describe the spread of a set of exam marks. One mark in the data set is much lower than all the others (an outlier).
(Total for Question 2 is 2 marks)
3
The ages, in years, of 9 people running a charity race are, in order:

19, 22, 24, 24, 27, 29, 31, 34, 38

Write down the median age.
(Total for Question 3 is 1 mark)
4
The number of text messages sent in a day by 8 students are:

12, 30, 8, 21, 15, 30, 18, 24

Find the median number of text messages.
(Total for Question 4 is 2 marks)
5
The marks, out of 20, of 12 students in a quiz are shown below, already arranged in order:

6, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 19
(a)Find the lower quartile.(1)
(b)Find the median.(1)
(c)Find the upper quartile.(1)
(d)Calculate the interquartile range.(1)
(Total for Question 5 is 4 marks)
6
The times, in seconds, taken by 16 runners to complete an obstacle course are shown below, in order:

12, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 25, 27

For n data values, the position of the lower quartile can be estimated using n/4, the position of the median using n/2, and the position of the upper quartile using 3n/4.
(a)Use n/4 to find the position of the lower quartile, and hence write down the lower quartile.(2)
(b)Find the median.(1)
(c)Find the upper quartile.(1)
(d)Calculate the interquartile range.(1)
(Total for Question 6 is 5 marks)
7
The number of texts sent in a day by 13 students are shown below, in order:

2, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 20, 24
(a)Explain why the position of the lower quartile is the 4th value, and write down the lower quartile.(2)
(b)Find the median.(1)
(c)Find the upper quartile.(1)
(d)Calculate the interquartile range.(1)
(Total for Question 7 is 5 marks)
8
The stem-and-leaf diagram shows the time, in minutes, spent on homework by 20 students.
StemLeaves
05 8 9
10 1 2 4 6 7 8 9
20 2 3 5 7 9
31 3 4

Key: 1 | 2 means 12 minutes
(a)Find the median time.(1)
(b)Find the lower quartile.(1)
(c)Find the upper quartile.(1)
(d)Calculate the interquartile range.(1)
(Total for Question 8 is 4 marks)
9
Two classes sat the same maths test, out of 100. The ordered scores were:

Class A: 45, 52, 58, 61, 63, 67, 70, 72, 78, 85
Class B: 50, 55, 60, 62, 64, 66, 68, 70, 74, 90
(a)Calculate the interquartile range for Class A.(2)
(b)Calculate the interquartile range for Class B.(2)
(c)Both classes have a median score of 65. Compare the spread of test scores in Class A and Class B.(2)
(Total for Question 9 is 6 marks)
10
As part of a statistical enquiry into how long online returns take, a company timed 80 customers completing the return process. The grouped frequency table shows the results.
Time taken, t (minutes)FrequencyCumulative frequency
0 < t ≤ 588
5 < t ≤ 1020?
10 < t ≤ 1524?
15 < t ≤ 2016?
20 < t ≤ 2512?
(a)Complete the cumulative frequency column of the table.(2)
(b)Which stage of the statistical enquiry cycle (plan, collect, process or interpret) does building this cumulative frequency table represent? Give a reason for your answer.(1)
(Total for Question 10 is 3 marks)
11
The cumulative frequency graph shows the results from Question 10, for the times taken by 80 customers to complete an online return.
01020304050607080 0510152025 Time taken, t (minutes) Cumulative frequency
(a)Use the graph to estimate the median time taken.(2)
(b)Use the graph to estimate the lower quartile.(1)
(c)Use the graph to estimate the upper quartile.(1)
(d)Hence calculate an estimate for the interquartile range.(1)
(Total for Question 11 is 5 marks)
12
Using your estimates from Question 11 (lower quartile 8 minutes, median 12.5 minutes, upper quartile 17.5 minutes), and given that the fastest customer completed their return in 2 minutes and the slowest took 24 minutes, draw a box plot on the grid provided to show this information.
0510152025 Time taken, t (minutes)
(Total for Question 12 is 3 marks)
13
A rival company, Company B, also recorded how long its customers took to complete online returns. The box plot below shows the results for Company B, together with the box plot for Company A from Question 12.
Company A Company B 051015202530 Time taken, t (minutes)
(a)Write down the median return time for Company B.(1)
(b)Calculate the interquartile range for Company B.(2)
(c)Compare the return times for Company A and Company B, using the medians and interquartile ranges.(2)
(Total for Question 13 is 5 marks)
14
The masses, in kg, of 11 parcels handled by a delivery depot are, in order:

2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 15
(a)Show that the lower quartile is 3 kg and the upper quartile is 7 kg.(2)
(b)A parcel is considered an outlier if its mass is more than 1.5 x IQR above the upper quartile. Determine, showing your working, whether the parcel weighing 15 kg is an outlier.(2)
(Total for Question 14 is 4 marks)
15
The grouped frequency table shows the waiting times, in minutes, of 60 patients at a clinic.
Waiting time, w (minutes)Frequency
0 < w ≤ 105
10 < w ≤ 2020
20 < w ≤ 3010
30 < w ≤ 4020
40 < w ≤ 505
(a)Write down the class interval that contains the median.(1)
(b)Use linear interpolation to estimate the median waiting time.(3)
(Total for Question 15 is 4 marks)
16
Using the waiting time table from Question 15 (60 patients; cumulative frequencies 5, 25, 35, 55, 60 at 10, 20, 30, 40, 50 minutes):
(a)Use linear interpolation to estimate the lower quartile.(2)
(b)Use linear interpolation to estimate the upper quartile.(2)
(c)Hence calculate an estimate for the interquartile range.(1)
(Total for Question 16 is 5 marks)
17
A second clinic, Clinic B, records the waiting times, in minutes, of 50 patients.
Waiting time, w (minutes)Frequency
0 < w ≤ 106
10 < w ≤ 2016
20 < w ≤ 3014
30 < w ≤ 4010
40 < w ≤ 504
(a)Use linear interpolation to estimate the lower quartile of the waiting times at Clinic B.(2)
(b)Use linear interpolation to estimate the upper quartile, and hence find the interquartile range, for Clinic B.(2)
(c)Compare the waiting times at Clinic A (Question 16) and Clinic B, using the interquartile ranges.(2)
(Total for Question 17 is 6 marks)
Mark scheme · S12 Median Quartiles and IQR

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