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Date	May Example questions	Marks available	4	Reference code	EXM.2.SL.TZ0.1
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find and Estimate	Question number	1	Adapted from	N/A

Question

The principal of a high school is concerned about the effect social media use might be having on the self-esteem of her students. She decides to survey a random sample of 9 students to gather some data. She wants the number of students in each grade in the sample to be, as far as possible, in the same proportion as the number of students in each grade in the school.

The number of students in each grade in the school is shown in table.

In order to select the 3 students from grade 12, the principal lists their names in alphabetical order and selects the 28^th, 56^th and 84^th student on the list.

Once the principal has obtained the names of the 9 students in the random sample, she surveys each student to find out how long they used social media the previous day and measures their self-esteem using the Rosenberg scale. The Rosenberg scale is a number between 10 and 40, where a high number represents high self-esteem.

State the name for this type of sampling technique.

[1]

Show that 3 students will be selected from grade 12.

[3]

b.i.

Calculate the number of students in each grade in the sample.

[2]

b.ii.

State the name for this type of sampling technique.

[1]

Calculate Pearson’s product moment correlation coefficient, $r$ .

[2]

d.i.

Interpret the meaning of the value of $r$ in the context of the principal’s concerns.

[1]

d.ii.

Explain why the value of $r$ makes it appropriate to find the equation of a regression line.

[1]

d.iii.

Another student at the school, Jasmine, has a self-esteem value of 29.

By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.

[4]

Markscheme

Stratified sampling A1

[1 mark]

There are 260 students in total A1

$\frac{{84}}{{260}} \times 9 = 2.91$ M1A1

So 3 students will be selected. AG

[3 marks]

b.i.

grade 9 $= \frac{{60}}{{260}} \times 9 \approx 2$ , grade 10 $= \frac{{83}}{{260}} \times 9 \approx 3$ , grade 11 $= \frac{{33}}{{260}} \times 9 \approx 1$ A2

[2 marks]

b.ii.

Systematic sampling A1

[1 mark]

$r = -0.901$ A2

[2 marks]

d.i.

The negative value of $r$ indicates that more time spent on social media leads to lower self-esteem, supporting the principal’s concerns. R1

[1 mark]

d.ii.

$r$ being close to –1 indicates there is strong correlation, so a regression line is appropriate. R1

[1 mark]

d.iii.

Find the regression line of $t$ on $s$ . M1

$t = - 0.281s + 9.74$ A1

$t = \left( { - 0.2807 \ldots } \right)\left( {29} \right) + 9.739 \ldots = 1.60$ hours M1A1

[4 marks]

Examiners report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

d.i.

[N/A]

d.ii.

[N/A]

d.iii.

[N/A]

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques

Show 29 related questions

EXM.1.SL.TZ0.2c:
Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.
EXM.2.SL.TZ0.1c:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1a:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1d.i:
Calculate Pearson’s product moment correlation coefficient, $r$ .
18M.1.SL.TZ1.S_2a:
Find the value of the interquartile range.
19M.2.SL.TZ1.S_3b:
The graph of $f$ has a horizontal tangent line at $x = 0$ and at $x = a$ . Find $a$ .
17M.2.SL.TZ1.S_1b.i:
Find the mean.
17M.2.SL.TZ2.S_8b.i:
Write down the coordinates of A.
17M.2.SL.TZ2.S_8c.i:
Find the coordinates of B.
EXM.2.SL.TZ0.1b.i:
Show that 3 students will be selected from grade 12.
EXM.2.SL.TZ0.1d.iii:
Explain why the value of $r$ makes it appropriate to find the equation of a regression line.
EXM.2.SL.TZ0.1b.ii:
Calculate the number of students in each grade in the sample.
EXM.1.SL.TZ0.2b:
Hence, show that a data set with only 5 numbers in it cannot have any outliers.
17M.2.SL.TZ2.S_8b.ii:
Write down the rate of change of $f$ at A.
EXM.2.SL.TZ0.1d.ii:
Interpret the meaning of the value of $r$ in the context of the principal’s concerns.
EXM.1.SL.TZ0.2a:
Recalling definitions, such as the Lower Quartile is the $\frac{{n + 1}}{4}th$ piece of data with the data placed in order, find an expression for the Interquartile Range.
17M.2.SL.TZ2.S_8a:
Find the value of $p$ .
17M.2.SL.TZ2.S_8d:
Let $R$ be the region enclosed by the graph of $f$ , the $x$ -axis, the line $x = b$ and the line $x = a$ . The region $R$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
17M.2.SL.TZ1.S_1a.ii:
Find the value of the range.
22M.2.SL.TZ2.5b:
Verify that the measurement of $0.46$ seconds is not an outlier.
17M.2.SL.TZ1.S_1a.i:
Write down the mode.
21M.1.SL.TZ1.4b:
Hence, find the minimum possible value of $L$ .
18M.1.SL.TZ1.S_2b:
One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.
17M.2.SL.TZ2.S_8c.ii:
Find the the rate of change of $f$ at B.
21M.1.SL.TZ2.7e.i:
Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.
21M.1.SL.TZ2.7e.ii:
Suggest a more appropriate sampling method.
21M.1.SL.TZ1.4a:
Find the minimum possible value of $U$ .
22M.1.SL.TZ1.3a:
Find the largest value of $c$ that would not be considered an outlier.
17M.2.SL.TZ1.S_1b.ii:
Find the variance.

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Topic 4—Statistics and probability » SL 4.10—X on y regression line

Topic 4—Statistics and probability

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Markscheme

Examiners report

Syllabus sections

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