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

Question

A data set consisting of $16$ $16$ test scores has mean $14.5$ $14.5$ . One test score of $9$ $9$ requires a second marking and is removed from the data set.

Find the mean of the remaining $15$ $15$ test scores.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$\frac{16 Σ i = 1 x_{i}}{16} = 14.5$ $\frac{Σ_{i = 1}^{16} x_{i}}{16} = 14.5$ (M1)

Note: Award M1 for use of $¯ x = \frac{n Σ i = 1 x_{i}}{n}$ $\bar{x} = \frac{Σ_{i = 1}^{n} x_{i}}{n}$ .

$\Rightarrow 16 Σ i = 1 x_{i} = 232$ $\Rightarrow Σ_{i = 1}^{16} x_{i} = 232$ (A1)

new $¯ x = \frac{232 - 9}{15}$ $\bar{x} = \frac{232 - 9}{15}$ (A1)

$= 14.9 (= 14.8 ¯ 6, = \frac{223}{15})$ $= 14.9 (= 14.8 \bar{6}, = \frac{223}{15})$ A1

Note: Do not accept 15.

[4 marks]

Examiners report

[N/A]

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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17M.1.SL.TZ2.T_7c:
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Find μ, the expected value of X.
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Find the value of $b$ $b$ .
20N.1.SL.TZ0.T_7b:
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20N.1.SL.TZ0.T_7c:
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18M.1.AHL.TZ2.H_3b.ii:
Find P(X > μ).
16N.2.SL.TZ0.S_8c:
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Find the probability that it will take Fiona between $15$ $15$ minutes and $30$ $30$ minutes to walk to the bus stop.
19M.2.AHL.TZ1.H_3c:
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22M.2.SL.TZ1.2a:
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19M.1.SL.TZ1.T_2d.i:
For these eight animals find the mean speed.
17N.1.SL.TZ0.T_1a.ii:
For the students in this group write down the median age.
19M.2.SL.TZ1.T_3f:
Write down the number of degrees of freedom for this test.
16N.1.SL.TZ0.T_2b:
Draw a box-and-whisker diagram on the grid below to represent the Vitamin C content, in milligrams, for this sample.
19M.1.SL.TZ2.T_6a:
State what 13 represents in the given diagram.
17N.2.SL.TZ0.T_1c.i:
Use your graphic display calculator to estimate the mean of $N$ $N$ ;
18M.2.SL.TZ1.T_2e:
State, with a reason, whether you would reject the null hypothesis.
16N.2.SL.TZ0.T_1c:
Plot the point $(¯ x, ¯ y)$ $(\bar x,{\text{ }}\bar y)$ on your scatter diagram and label this point M.
17M.1.SL.TZ2.T_7b:
Using the mean score, write down a second equation in terms of $x$ $x$ and $y$ $y$ .
20N.1.SL.TZ0.T_3c:
On the grid below, draw a histogram for the data in the table.
16N.2.SL.TZ0.T_1e:
Write down the equation of the regression line $y$ $y$ on $x$ $x$ for these eight male students.
17N.1.SL.TZ0.T_1b:
Draw a box-and-whisker diagram, for these students’ ages, on the following grid.
17M.1.SL.TZ2.T_7a:
Write down an equation, in terms of $x$ $x$ and $y$ $y$ , for the total number of times the die was rolled.
18M.1.SL.TZ2.S_3a:
Find n.
19M.2.SL.TZ1.S_1a:
For these data, find the mean distance from a student’s home to school.
17M.2.SL.TZ1.S_1b.ii:
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19M.1.SL.TZ2.S_8d.ii:
Find the mean number of hours that all 30 girls and boys spent watching television that week.
18M.2.SL.TZ1.T_2h:
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Find the probability that each of these flights travelled at least 5000 km.
17N.2.SL.TZ0.T_1g:
State the result of the test. Give a reason for your answer.
16N.2.SL.TZ0.S_8b:
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18M.1.SL.TZ1.T_6c.ii:
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18M.1.SL.TZ2.S_3b.ii:
Find the value of the new variance.
20N.1.SL.TZ0.S_8a:
Find the value of $a$ $a$ .
20N.1.SL.TZ0.S_8e:
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18M.2.SL.TZ1.T_2b:
Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
16N.2.SL.TZ0.S_8a:
Find the mean number of hours spent browsing the Internet.
18M.1.SL.TZ1.T_2b.ii:
Find the interquartile range.
18M.1.SL.TZ2.T_12b.ii:
Calculate the value of k.
17N.2.SL.TZ0.T_1b.ii:
Write down, for $N$ $N$ , the mid-interval value of the modal class.
19M.2.SL.TZ1.T_3e.ii:
State the alternative hypothesis.
18M.1.SL.TZ1.T_2a:
Find the value of x.
18M.2.SL.TZ1.T_2c:
Write down the number of degrees of freedom.
17M.2.SL.TZ1.T_5f.ii:
Calculate the expected number of students that spent at least 90 minutes preparing for the test.
17N.2.SL.TZ0.T_1a:
State whether $N$ $N$ is a discrete or a continuous variable.
17N.2.SL.TZ0.T_1f.ii:
Write down the $χ^{2}$ ${\chi ^2}$ statistic.
16N.2.SL.TZ0.T_1d:
Write down the value of $r$ $r$ , the Pearson’s product–moment correlation coefficient, for these data.
19M.2.SL.TZ1.T_3d:
Write down the ratio of teenagers to non-teenagers in its simplest form.
17N.1.SL.TZ0.T_1a.i:
For the students in this group find the mean age;
20N.1.SL.TZ0.T_7d.i:
Using your answers to parts (b) and (c), find the height of Flower $A$ $A$ .
19M.2.SL.TZ1.T_3g:
Calculate the expected number of teenagers that prefer cats.
17M.2.SL.TZ1.T_5a.i:
Calculate the mean test grade of the students;
20N.1.SL.TZ0.T_7a:
Find the height of Flower null.
16N.1.SL.TZ0.T_2a:
Giving your answer to one decimal place, write down the value of

(i) the median level of Vitamin C content of the oranges in the sample;

(ii) the lower quartile;

(iii) the upper quartile.
17M.2.SL.TZ1.T_5e:
Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.
20N.1.SL.TZ0.T_3a:
Write down the modal group for these data.
17M.2.SL.TZ1.T_5d:
Find the probability that this student scored a grade 5 or higher.
18M.2.SL.TZ1.T_2f:
Write down the probability that this flight arrived on time.
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Use your graphic display calculator to estimate the standard deviation of $N$ $N$ .
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Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.
17N.2.SL.TZ0.T_1e.i:
Write down the null hypothesis for this test;
17N.2.SL.TZ0.T_1e.ii:
Write down the number of degrees of freedom.
19M.2.SL.TZ1.T_3h:
Use your graphic display calculator to find the $p$ $p$ -value for this test.
18N.2.SL.TZ0.T_3a.ii:
Find the interquartile range.
18N.2.SL.TZ0.T_3c.i:
Write down the modal class.
18N.2.SL.TZ0.T_3c.ii:
Write down the mid-interval value of the modal class.
18N.2.SL.TZ0.T_3e:
The teacher sets a grade boundary that is one standard deviation below the mean.

Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary.
18M.2.SL.TZ2.T_2a:
Find the number of buses that travelled a distance between 15000 and 20000 kilometres.
16N.2.SL.TZ0.T_1a:
On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the $x$ $x$ -axis and 2 cm to represent 10 points on the $y$ $y$ -axis.
16N.2.SL.TZ0.T_1b:
(i) $¯ x$ ${\bar x}$ , the mean number of hours spent on social media;

(ii) $¯ y$ ${\bar y}$ , the mean number of IB Diploma points.
16N.2.SL.TZ0.T_1f:
Draw the regression line, from part (e), on your scatter diagram.
16N.2.SL.TZ0.T_1g:
Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.
17M.2.SL.TZ1.T_5a.ii:
Calculate the standard deviation.
17M.2.SL.TZ1.T_5c:
Find the interquartile range.
17M.2.SL.TZ1.T_5f.i:
Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.
19M.2.SL.TZ1.T_3i:
State the conclusion for this test. Give a reason for your answer.

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Topic 4—Statistics and probability

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