17M.1.SL.TZ2.T_6

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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]

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

[1]

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 / solution

* 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]

40 (leaves) (A1) (C1)

[1 mark]

$(200 \times 0.90 = ){\text{ }}180$ 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).

$(k = ){\text{ }}10.5{\text{ (cm)}}$ (A1) (C2)

Note: Accept an error of ±0.1.

[2 marks]

c.i.

$\left| {\frac{{9.5 - 10.5}}{{10.5}}} \right| \times 100\%$ (M1)

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

${\text{9.52 (% ) }}\left( {{\text{9.52380}} \ldots {\text{ (% )}}} \right)$ (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]

c.i.

[N/A]

c.ii.