Date | May Specimen paper | Marks available | 1 | Reference code | SPM.1.SL.TZ0.7 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | Write down | Question number | 7 | Adapted from | N/A |
Question
A large company surveyed 160 of its employees to find out how much time they spend traveling to work on a given day. The results of the survey are shown in the following cumulative frequency diagram.
Only 10% of the employees spent more than minutes traveling to work.
The results of the survey can also be displayed on the following box-and-whisker diagram.
Find the median number of minutes spent traveling to work.
Find the number of employees whose travelling time is within 15 minutes of the median.
Find the value of .
Write down the value of .
Find the value of .
Hence, find the interquartile range.
Travelling times of less than minutes are considered outliers.
Find the value of .
Markscheme
evidence of median position (M1)
80th employee
40 minutes A1
[2 marks]
valid attempt to find interval (25–55) (M1)
18 (employees), 142 (employees) A1
124 A1
[3 marks]
recognising that there are 16 employees in the top 10% (M1)
144 employees travelled more than minutes (A1)
= 56 A1
[3 marks]
= 70 A1
[1 mark]
recognizing is first quartile value (M1)
40 employees
= 33 A1
[2 marks]
47 − 33 (M1)
IQR = 14 A1
[2 marks]
attempt to find 1.5 × their IQR (M1)
33 − 21
12 (A1)
[2 marks]