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Date	May 2021	Marks available	2	Reference code	21M.2.SL.TZ1.1
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 1
Command term	Copy and Complete	Question number	1	Adapted from	N/A

Question

As part of his mathematics exploration about classic books, Jason investigated the time taken by students in his school to read the book The Old Man and the Sea. He collected his data by stopping and asking students in the school corridor, until he reached his target of $10$ $10$ students from each of the literature classes in his school.

Jason constructed the following box and whisker diagram to show the number of hours students in the sample took to read this book.

Mackenzie, a member of the sample, took $25$ $25$ hours to read the novel. Jason believes Mackenzie’s time is not an outlier.

For each student interviewed, Jason recorded the time taken to read The Old Man and the Sea $(x)$ $(x)$ , measured in hours, and paired this with their percentage score on the final exam $(y)$ $(y)$ . These data are represented on the scatter diagram.

Jason correctly calculates the equation of the regression line $y$ $y$ on $x$ $x$ for these students to be

$y = - 1.54 x + 98.8$ $y = - 1.54 x + 98.8$ .

He uses the equation to estimate the percentage score on the final exam for a student who read the book in $1.5$ $1.5$ hours.

Jason found a website that rated the ‘top $50$ $50$ ’ classic books. He randomly chose eight of these classic books and recorded the number of pages. For example, Book $H$ $H$ is rated $44 th$ $44 th$ and has $281$ $281$ pages. These data are shown in the table.

Jason intends to analyse the data using Spearman’s rank correlation coefficient, $r_{s}$ $r_{s}$ .

State which of the two sampling methods, systematic or quota, Jason has used.

[1]

Write down the median time to read the book.

[1]

Calculate the interquartile range.

[2]

Determine whether Jason is correct. Support your reasoning.

[4]

Describe the correlation.

[1]

Find the percentage score calculated by Jason.

[2]

State whether it is valid to use the regression line $y$ $y$ on $x$ $x$ for Jason’s estimate. Give a reason for your answer.

[2]

Copy and complete the information in the following table.

[2]

Calculate the value of $r_{s}$ $r_{s}$ .

[2]

i.i.

Interpret your result.

[1]

i.ii.

Markscheme

Quota sampling A1

[1 mark]

$10$ $10$ (hours) A1

[1 mark]

$15 - 7$ $15 - 7$ (M1)

Note: Award M1 for $15$ $15$ and $7$ $7$ seen.

$8$ $8$ A1

[2 marks]

indication of a valid attempt to find the upper fence (M1)

$15 + 1.5 \times 8$ $15 + 1.5 \times 8$

$27$ $27$ A1

$25 < 27$ $25 < 27$ (accept equivalent answer in words) R1

Jason is correct A1

Note: Do not award R0A1. Follow through within this part from their $27$ $27$ , but only if their value is supported by a valid attempt or clearly and correctly explains what their value represents.

[4 marks]

“negative” seen A1

Note: Strength cannot be inferred visually; ignore “strong” or “weak”.

[1 mark]

correct substitution (M1)

$y = - 1.54 \times 1.5 + 98.8$ $y = - 1.54 \times 1.5 + 98.8$

$96.5 (%) (96.49)$ $96.5 (%) (96.49)$ A1

[2 marks]

not reliable A1

extrapolation OR outside the given range of the data R1

Note: Do not award A1R0. Only accept reasoning that includes reference to the range of the data. Do not accept a contextual reason such as $1.5$ $1.5$ hours is too short to read the book.

[2 marks]

A1A1

Note: Do not award A1 for correct ranks for ‘number of pages’. Award A1 for correct ranks for ‘top 50 rating’.

[2 marks]

$0.714 (0.714285 \dots)$ $0.714 (0.714285 \dots)$ A2