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Date May 2019 Marks available 2 Reference code 19M.1.SL.TZ2.S_8
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number S_8 Adapted from N/A

Question

A group of 10 girls recorded the number of hours they spent watching television during a particular week. Their results are summarized in the box-and-whisker plot below.

The group of girls watched a total of 180 hours of television.

A group of 20 boys also recorded the number of hours they spent watching television that same week. Their results are summarized in the table below.

The following week, the group of boys had exams. During this exam week, the boys spent half as much time watching television compared to the previous week.

For this exam week, find

The range of the data is 16. Find the value of a .

[2]
a.

Find the value of the interquartile range.

[2]
b.

Find the mean number of hours that the girls in this group spent watching television that week.

[2]
c.

Find the total number of hours the group of boys spent watching television that week.

[2]
d.i.

Find the mean number of hours that all 30 girls and boys spent watching television that week.

[3]
d.ii.

the mean number of hours that the group of boys spent watching television.

[2]
e.i.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach       (M1)

eg    16 + 8,  a − 8

24 (hours)       A1 N2

[2 marks]

a.

valid approach       (M1)

eg    20 − 15,  Q 3 Q 1 ,  15 − 20

IQR = 5       A1 N2

[2 marks]

b.

correct working      (A1)

eg     180 10 ,   180 n ,   x 10

mean = 18 (hours)      A1 N2

[2 marks]

c.

attempt to find total hours for group B     (M1)

eg     x ¯ × n

group B total hours = 420  (seen anywhere)     A1 N2

[2 marks]

d.i.

attempt to find sum for combined group (may be seen in working)      (M1)

eg    180 + 420,  600

correct working        (A1)

eg    180 + 420 30 600 30

mean = 20 (hours)    A1 N2

[3 marks]

d.ii.

valid approach to find the new mean     (M1)

eg    1 2 μ 1 2 × 21  

mean = 21 2  (= 10.5) hours    A1 N2

[2 marks]

e.i.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
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Topic 4—Statistics and probability

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