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Date May Specimen paper Marks available 2 Reference code SPM.1.SL.TZ0.7
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Find 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 k 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.

[2]
a.

Find the number of employees whose travelling time is within 15 minutes of the median.

[3]
b.

Find the value of  k .

[3]
c.

Write down the value of b .

[1]
d.

Find the value of a .

[2]
e.i.

Hence, find the interquartile range.

[2]
e.ii.

Travelling times of less than p minutes are considered outliers.

Find the value of p .

[2]
f.

Markscheme

evidence of median position         (M1)

80th employee

40 minutes       A1

[2 marks]

a.

valid attempt to find interval (25–55)      (M1)

18 (employees), 142 (employees)      A1

124      A1

[3 marks]

b.

recognising that there are 16 employees in the top 10%     (M1)

144 employees travelled more than k minutes       (A1)

k = 56      A1

[3 marks]

c.

b = 70      A1

[1 mark]

d.

recognizing a is first quartile value      (M1)

40 employees

a = 33      A1

[2 marks]

e.i.

47 − 33       (M1)

IQR = 14      A1

[2 marks]

e.ii.

attempt to find 1.5 × their IQR      (M1)

33 − 21

12       (A1)

[2 marks]

f.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.i.
[N/A]
e.ii.
[N/A]
f.

Syllabus sections

Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
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Topic 4—Statistics and probability

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