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Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ2.T_6
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 2
Command term Write down Question number T_6 Adapted from N/A

Question

For a study, a researcher collected 200 leaves from oak trees. After measuring the lengths of the leaves, in cm, she produced the following cumulative frequency graph.

M17/5/MATSD/SP1/ENG/TZ2/06

The researcher finds that 10% of the leaves have a length greater than k cm.

Write down the median length of these leaves.

[1]
a.

Write down the number of leaves with a length less than or equal to 8 cm.

[1]
b.

Use the graph to find the value of k .

[2]
c.i.

Before measuring, the researcher estimated k to be approximately 9.5 cm. Find the percentage error in her estimate.

[2]
c.ii.

Markscheme

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

9 (cm)     (A1)     (C1)

[1 mark]

a.

40 (leaves)     (A1)     (C1)

[1 mark]

b.

( 200 × 0.90 = )   180 or equivalent     (M1)

 

Note:     Award (M1) for a horizontal line drawn through the cumulative frequency value of 180 and meeting the curve (or the corresponding vertical line from 10.5 cm).

 

( k = )   10.5  (cm)     (A1)     (C2)

 

Note:     Accept an error of ±0.1.

 

[2 marks]

c.i.

| 9.5 10.5 10.5 | × 100 %     (M1)

 

Notes:     Award (M1) for their correct substitution into the percentage error formula.

 

9.52 (% )  ( 9.52380  (% ) )     (A1)(ft)     (C2)

 

Notes:     Follow through from their answer to part (c)(i).

Award (A1)(A0) for an answer of 9.52 with or without working.

 

[2 marks]

c.ii.

Examiners report

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

Syllabus sections

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

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