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2.5

1a. [1 mark]

Markscheme

3 (A1) (C1)

[1 mark]

Examiners report

[N/A]

1b. [3 marks]

Markscheme

median is 13th position (M1)

CF: 2, 6, 14, 20, 23, 25 (M1)

median = 3 (A1) (C3)

[3 marks]

Examiners report

[N/A]

1c. [1 mark]

Markscheme

2.5 (A1) (C1)

Note: Award (A1)(ft) if the sum of their parts (c)(i) and (c)(ii) is 4.

[1 mark]1

Examiners report

[N/A]

1d. [1 mark]

Markscheme

1.5 (A1)(ft) (C1)

Note: Award (A1)(ft) if the sum of their parts (c)(i) and (c)(ii) is 4.

[1 mark]

Examiners report

[N/A]

2a. [2 marks]

Markscheme

60 (A2)

[2 marks]

Examiners report

[N/A]

2b. [3 marks]

Markscheme

68 − 48 (A1)(M1)

Note: Award (A1) for two correct quartiles seen, (M1) for finding the difference between their two

quartiles.

2

= 20 (A1)(ft)(G3)

[3 marks]

Examiners report

[N/A]

2c. [2 marks]

Markscheme

3200 − 350 = 2850 (M1)

Note: Award (M1) for 2850 seen. Follow through from their 3200.

(Top grade boundary =) 76 (A1)(ft)(G2)

[2 marks]

Examiners report

[N/A]

2d. [2 marks]

Markscheme

60 < x ≤ 80 (A1)(A1)

Note: Award (A1) for 60, 80 seen, (A1) for correct strict and weak inequalities.

[2 marks]

Examiners report

[N/A]

2e. [1 mark]

3

Markscheme

70 (A1)(ft)

Note: Follow through from part (c)(i).

[1 mark]

Examiners report

[N/A]

2f. [2 marks]

Markscheme

57.2 (57.1875) (A2)(ft)

Note: Follow through from part (c)(ii).

[2 marks]

Examiners report

[N/A]

2g. [1 mark]

Markscheme

18.496 (A1)

Note: Award (A0) for 18.499.

[1 mark]

Examiners report

[N/A]

2h. [3 marks]

4

Markscheme

57.2 − 18.5 (M1)

= 38.7 (38.6918…) (A1)(ft)

Note: Award (M1) for subtracting their standard deviation from their mean. Follow through from part

(d) even if no working is shown.

450 (students) (A1)(ft)(G2)

Note: Accept any answer within the range of 450 to 475, inclusive. Follow through from part (d),

adjusting the acceptable range as necessary.

[3 marks]

Examiners report

[N/A]

3a. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution into median formula or for arranging all 9 values into

ascending/descending order.

(A1) (C2)

[2 marks]

Examiners report

[N/A]

3b. [2 marks]

Markscheme

5

2.69 (2.69072…) (A2)(ft)

Note: Follow through from part (a).

[2 marks]

Examiners report

[N/A]

3c. [2 marks]

Markscheme

13 − 8 (M1)

Note: Award (M1) for 13 and 8 seen.

= 5 (A1)(ft) (C4)

Note: Follow through from part (a).

[2 marks]

Examiners report

[N/A]

4a. [1 mark]

Markscheme

180 (A1) (C1)

[1 mark]

Examiners report

[N/A]

4b. [2 marks]

Markscheme

36, 24 (A1)(A1) (C2)

Note: Award (A0)(A1) for two incorrect values that add up to 60.

6

[2 marks]

Examiners report

[N/A]

4c. [1 mark]

Markscheme

125 (accept 125.5) (A1)

Examiners report

[N/A]

4d. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution of their mid-interval values, multiplied by their frequencies,

into mean formula.

=156 (155.625) (A1)(ft) (C3)

Note: Follow through from parts (b) and (c)(i).

[3 marks]

Examiners report

[N/A]

5a. [1 mark]

Markscheme

12.5 (A1) (C1)

[1 mark]

Examiners report

[N/A]

7

5b. [1 mark]

Markscheme

33 + k OR 10 + 8 + 5 + 10 + k (A1)

Note: Award (A1) for “number of customers = 33 + k”.

[1 mark]

Examiners report

[N/A]

5c. [3 marks]

Markscheme

(M1)(A1)(ft)

Note: Award (M1) for substitution into the mean formula and equating to 12, (A1)(ft) for their correct

substitutions.

(k =) 7 (A1)(ft) (C4)

Note: Follow through from part (b)(i) and their mid-interval values, consistent with part (a). Do not

award final (A1) if answer is not an integer.

[3 marks]

Examiners report

[N/A]

5d. [1 mark]

Markscheme

8

(A1)(ft) (C1)

Note: Follow through from their part (b)(ii) but only if the value is between 1 and 10, inclusive.

[1 mark]

Examiners report

[N/A]

6a. [1 mark]

Markscheme

The arrival status is dependent on the distance travelled by the incoming flight (A1)

Note: Accept “associated” or “not independent”.

[1 mark]

9

Examiners report

[N/A]

6b. [2 marks]

Markscheme

OR (M1)

Note: Award (M1) for correct substitution into expected value formula.

= 15 (A1) (G2)

[2 marks]

Examiners report

[N/A]

6c. [1 mark]

Markscheme

4 (A1)

Note: Award (A0) if “2 + 2 = 4” is seen.

[1 mark]

Examiners report

[N/A]

6d. [2 marks]

Markscheme

9.55 (9.54671…) (G2)

Note: Award (G1) for an answer of 9.54.

[2 marks]

Examiners report

[N/A] 10

6e. [1 mark]

Markscheme

0.0488 (0.0487961…) (G1)

[1 mark]

Examiners report

[N/A]

6f. [2 marks]

Markscheme

Reject the Null Hypothesis (A1)(ft)

Note: Follow through from their hypothesis in part (a).

9.55 (9.54671…) > 7.779 (R1)(ft)

OR

0.0488 (0.0487961…) < 0.1 (R1)(ft)

Note: Do not award (A1)(ft)(R0)(ft). Follow through from part (d). Award (R1)(ft) for a correct

comparison, (A1)(ft) for a consistent conclusion with the answers to parts (a) and (d). Award (R1)(ft)

for χ2calc > χ2

crit , provided the calculated value is explicitly seen in part (d)(i).

[2 marks]

Examiners report

[N/A]

6g. [2 marks]

Markscheme

(A1)(A1) (G2)

Note: Award (A1) for correct numerator, (A1) for correct denominator.

[2 marks]

11

Examiners report

[N/A]

6h. [2 marks]

Markscheme

(A1)(A1) (G2)

Note: Award (A1) for correct numerator, (A1) for correct denominator.

[2 marks]

Examiners report

[N/A]

6i. [3 marks]

Markscheme

(A1)(M1)

Note: Award (A1) for two correct fractions and (M1) for multiplying their two fractions.

(A1) (G2)

[3 marks]

Examiners report

[N/A]

7a. [2 marks]

Markscheme

28 − 20 (A1)

Note: Award (A1) for 28 and 20 seen.

8 (A1)(G2)

[2 marks]

12

Examiners report

[N/A]

7b. [2 marks]

Markscheme

13500 (G2)

Note: Accept an answer in the range 13500 to 13750.

[2 marks]

Examiners report

[N/A]

7c. [1 mark]

Markscheme

10000 (G1)


[1 mark]

Examiners report

[N/A]

7d. [1 mark]

Markscheme

16000 (G1)


[1 mark]

Examiners report

[N/A]

7e. [1 mark]

13

Markscheme

6000 (A1)(ft)

Note: Follow through from their part (b)(ii) and (iii).

[1 mark]

Examiners report

[N/A]

7f. [1 mark]

Markscheme

25% (A1)

[1 mark]

Examiners report

[N/A]

7g. [1 mark]

Markscheme

11 (G1)

[1 mark]

Examiners report

[N/A]

7h. [2 marks]

Markscheme

30 − 8 OR 22 (M1)

Note: Award (M1) for subtracting 30 − 8 or 22 seen.

15750 (A1)(G2)

Note: Accept 15750 ± 250.

14

[2 marks]

Examiners report

[N/A]

7i. [4 marks]

Markscheme

(A1)(A1)(A1)(A1)

Note: Award (A1) for correct label and scale; accept “distance” or “km” for label.

(A1)(ft) for correct median,

(A1)(ft) for correct quartiles and box,

(A1) for endpoints at 2500 and 23 000 joined to box by straight lines.

Accept ±250 for the median, quartiles and endpoints.

Follow through from their part (b).

The final (A1) is not awarded if the line goes through the box.

[4 marks]

Examiners report

[N/A]

8a. [2 marks]

Markscheme

(M1)

15

Note: Award (M1) for correct substitutions into mean formula.

(A1) (C2)

[2 marks]

Examiners report

[N/A]

8b. [1 mark]

Markscheme

16.5 (A1) (C1)

[1 mark]

Examiners report

[N/A]

8c. [3 marks]

Markscheme

(A1)(A1)(A1)(ft) (C3)

Note: Award (A1) for correct endpoints, (A1) for correct quartiles, (A1)(ft) for their median. Follow

through from part (a)(ii), but only if median is between 16 and 18.5. If a horizontal line goes through

the box, award at most (A1)(A1)(A0). Award at most (A0)(A1)(A1) if a ruler has not been used.

16

[3 marks]

Examiners report

[N/A]

9a. [1 mark]

Markscheme

discrete (A1)

[1 mark]

Examiners report

[N/A]

9b. [1 mark]

Markscheme

(A1)

[1 mark]

Examiners report

[N/A]

9c. [1 mark]

Markscheme

15.5 (A1)(ft)

Note: Follow through from part (b)(i).

[1 mark]

Examiners report

17

[N/A]

9d. [2 marks]

Markscheme

(G2)

[2 marks]

Examiners report

[N/A]

9e. [1 mark]

Markscheme

(G1)

[1 marks]

Examiners report

[N/A]

9f. [2 marks]

Markscheme

OR (M1)

Note: Award (M1) for correct substitution into expected frequency formula.

(A1)(G2)

[2 marks]

Examiners report

[N/A]

18

9g. [1 mark]

Markscheme

choice of category and number of correct answers are independent (A1)

Notes: Accept “no association” between (choice of) category and number of correct answers. Do not

accept “not related” or “not correlated” or “influenced”.

[1 mark]

Examiners report

[N/A]

9h. [1 mark]

Markscheme

6 (A1)

[1 mark]

Examiners report

[N/A]

9i. [1 mark]

Markscheme

(G1)

[1 mark]

Examiners report

[N/A]

9j. [2 marks]

19

Markscheme

(G2)

[2 marks]

Examiners report

[N/A]

9k. [2 marks]

Markscheme

the null hypothesis is not rejected (the null hypothesis is accepted) (A1)(ft)

OR

(choice of) category and number of correct answers are independent (A1)(ft)

as OR (R1)

Notes: Award (R1) for a correct comparison of either their statistic to the critical value or their

-value to the significance level. Award (A1)(ft) from that comparison.

Follow through from part (f). Do not award (A1)(ft)(R0).

[2 marks]

Examiners report

[N/A]

10a. [1 mark]

Markscheme

or equivalent (A1) (C1)

[1 mark]

Examiners report20

[N/A]

10b. [2 marks]

Markscheme

or equivalent (M1)(A1) (C2)

Note: Award (M1) for a sum including and , divided by 100 and equated to 2.71, (A1) for a correct

equation.

[2 marks]

Examiners report

[N/A]

10c. [3 marks]

Markscheme

and (M1)

Note: Award (M1) for obtaining a correct linear equation in one variable from their (a) and their (b).

This may be implied if seen in part (a) or part (b).

(A1)(ft)(A1)(ft) (C3)

Notes: Follow through from parts (a) and (b), irrespective of working seen provided the answers are

positive integers.

[3 marks]

21

Examiners report

[N/A]

11a. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution into mean formula.

(A1) (G2)

[2 marks]

Examiners report

[N/A]

11b. [1 mark]

Markscheme

(G1)

[1 mark]

Examiners report

[N/A]

11c. [1 mark]

Markscheme

5 (A1)

[1 mark]

Examiners report

22

[N/A]

11d. [2 marks]

Markscheme

(M1)

Note: Award (M1) for 6 and 4 seen.

(A1) (G2)

[2 marks]

Examiners report

[N/A]

11e. [2 marks]

Markscheme

(M1)

Note: Award (M1) for seen.

(A1) (G2)

[2 marks]

Examiners report

[N/A]

11f. [3 marks]

Markscheme

23

(M1)(M1)

Note: Award (M1) for seen, (M1) for multiplying their first probability by .

OR

Note: Award (M1) for seen, (M1) for dividing their first probability by .

(A1)(ft) (G3)

Note: Follow through from part (d).

[3 marks]

Examiners report

[N/A]

11g. [2 marks]

Markscheme

(M1)

OR

24

(M1)

Note: Award (M1) for a diagram showing the correct shaded region .

(A1) (G2)

[2 marks]

Examiners report

[N/A]

11h. [2 marks]

Markscheme

(M1)

(A1)(ft) (G2)

Note: Follow through from part (f)(i).

[2 marks]

Examiners report

[N/A]

12a. [3 marks]

25

Markscheme

(i) 32.5 (A1)

(ii) 31.9 (A1)

(iii) 33.1 (A1) (C3)

Note: Answers must be given correct to 1 decimal place.

[3 marks]

Examiners report

[N/A]

12b. [3 marks]

Markscheme

Note: Award (A1)(ft) for correct median, (A1)(ft) for correct quartiles and box, (A1) for correct end

points of whiskers and straight whiskers.

Award at most (A1)(A1)(A0) if a horizontal line goes right through the box or if the whiskers are not

well aligned with the midpoint of the box.

Follow through from part (a).

[3 marks]

26

Examiners report

[N/A]

13a. [4 marks]

Markscheme

(A4)

Notes: Award (A1) for correct scale and labelled axes.

Award (A3) for 7 or 8 points correctly plotted,

(A2) for 5 or 6 points correctly plotted,

(A1) for 3 or 4 points correctly plotted.

Award at most (A0)(A3) if axes reversed.

Accept and sufficient for labelling.

If graph paper is not used, award (A0).

If an inconsistent scale is used, award (A0). Candidates’ points should be read from this scale where

possible and awarded accordingly.

27

A scale which is too small to be meaningful (ie mm instead of cm) earns (A0) for plotted points.

[4 marks]

Examiners report

[N/A]

13b. [2 marks]

Markscheme

(i) (A1)

(ii) (A1)

[2 marks]

Examiners report

[N/A]

13c. [2 marks]

Markscheme

correctly plotted on graph (A1)(ft)

this point labelled M (A1)

Note: Follow through from parts (b)(i) and (b)(ii).

Only accept M for labelling.

[2 marks]

Examiners report

[N/A]

13d. [2 marks]

28

Markscheme

(G2)

Note: Award (G1) for 0.973, without minus sign.

[2 marks]

Examiners report

[N/A]

13e. [2 marks]

Markscheme

(A1)(A1)(G2)

Notes: Award (A1) for and (A1) . Award a maximum of (A1)(A0) if answer is not an

equation.

[2 marks]

Examiners report

[N/A]

13f. [2 marks]

Markscheme

line on graph (A1)(ft)(A1)(ft)

Notes: Award (A1)(ft) for straight line that passes through their M, (A1)(ft) for line (extrapolated if

necessary) that passes through .

29

If M is not plotted or labelled, follow through from part (e).

[2 marks]

Examiners report

[N/A]

13g. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution.

19 (points) (A1)(G2)

[2 marks]

Examiners report

[N/A]

13h. [1 mark]

Markscheme

extrapolation (R1)

OR

34 hours is outside the given range of data (R1)

Note: Do not accept ‘outlier’.

[1 mark]

30

Examiners report

[N/A]

14a. [1 mark]

Markscheme

(A1)

[1 mark]

Examiners report

[N/A]

14b. [1 mark]

Markscheme

(A1)

[1 mark]

Examiners report

[N/A]

14c. [2 marks]

Markscheme

(M1)

Note: Award (M1) for an attempt to substitute their mid-interval values (consistent with their answer

to part (b)) into the formula for the mean.

Award (M1) where a table is constructed with their (consistent) mid-interval values listed along

with the frequencies.

(A1)(ft)(G2)

31

Note: Follow through from their answer to part (b).

[2 marks]

Examiners report

[N/A]

14d. [2 marks]

Markscheme

(A1)(A1)

[2 marks]

Examiners report

[N/A]

14e. [4 marks]

Markscheme

(i) (A1)

Note: Accept .

Accept any answer between and .

(Accept 21.5, but do not accept 21.)

(ii) (A1)

Note: Accept . Do not accept .

Answer must be an integer.

32

(iii) (M1)

(A1)(G2)

Notes: Award (M1) for subtraction from . Accept .

Answer must be an integer.

[4 marks]

Examiners report

[N/A]

15a. [1 mark]

Markscheme

discrete (A1) (C1)

[1 mark]

Examiners report

Most candidates could state whether the data was discrete or continuous and find the mode however

the calculations to find the mean, median and standard deviation appeared problematic for some

candidates. A significant number of candidates gave the mode as 37 rather than 0. Many did not appear

to use their graph and some obtained the incorrect value of 1.47 from their graphic display calculator.

15b. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

33





15c. [4 marks]

Markscheme

(i) (A2)

Note: Award (M1) for seen.

Accept or as a final answer if or seen.

��

(ii) (A1)

(iii) (A1) (C4)

[4 marks]

Examiners report





16a. [4 marks]

Markscheme

34

(A4)

Notes: Award (A1) for correct scale and labels (accept and ).

Award (A3) for or points plotted correctly.



Award at most (A1)(A2) if points are joined up.

If axes are reversed, award at most (A0)(A3).

35

If graph paper is not used, award at most (A1)(A0).

[4 marks]

Examiners report

This question was very well attempted by a significant majority of candidates. Many good and accurate

attempts at plotting a scatter diagram were seen in part (a). However, a minority of candidates chose

not to use graph paper but instead used their answer book. These candidates achieved, at most, one

mark for that part question. Many correct answers were seen in parts (b) and (d) reflecting good use of

the graphic display calculator. Whilst many candidates realized that the line of regression passes

through the point M, a significant number of candidates seemed to draw their line ‘by eye’ rather than

using the equation found in part (d) and, as a consequence for many, their straight line (or projected

line) did not fall within the required tolerances for the second mark. Many candidates understood the

requirements for part (f) and full marks were seen on a majority of scripts. Those candidates, however,

who used their graph instead scored, at most, two marks here. Many candidates seemed to be well-

drilled in giving a suitable reason in part (f) and ‘within the data range’ or a ‘strong correlation’ were

frequently seen. Percentage error caused very few problems for candidates and many correct answers

were seen in part (h).

16b. [2 marks]

Markscheme

(i) (G1)

(ii) (G1)

[2 marks]

Examiners report








36







16c. [1 mark]

Markscheme

plotted and labelled on the scatter diagram (A1)(ft)

Notes: Follow through from their part (b).

Accept as the label.

[1 mark]

Examiners report














16d. [3 marks]

37

Markscheme

(i) (G1)

(ii) (G1)(G1)

Notes: Award (G1) for , (G1) for .

Award (G1)(G0) if not written in the form of an equation.

OR

(G1)(G1)(ft)

Note: Award (G1) for , (G1) for their and .

[3 marks]

Examiners report














16e. [2 marks] 38

Markscheme

straight line drawn on the scatter diagram (A1)(ft)(A1)(ft)

Notes: The line must be straight for either of the two marks to be awarded.

Award (A1)(ft) passing through their plotted in (c).

Award (A1)(ft) for correct -intercept (between and ).

Follow through from their -intercept found in part (d).

If part (d) is used, award (A1)(ft) for their intercept .

[2 marks]

Examiners report














16f. [3 marks]

Markscheme

(M1)

39

Note: Award (M1) for substitution of into their regression line.

(A1)(ft)

Note: Follow through from part (d). If 3 sf values are used the value is .

(A1)(ft)(G2)

Notes: The final (A1) is awarded for their answer given correct to the nearest dollar.

Method, followed by the answer of earns (M1)(G2). It is not necessary to see the interim step.

Where the candidate uses their graph instead of the equation, and arrives at an answer other than

, award, at most, (G1)(ft).

If the candidate uses their graph and arrives at the required answer of , award (G2)(ft).

[3 marks]

Examiners report












40



16g. [1 mark]

Markscheme

is within the range of distances given in the data OR the correlation coefficient is close to . (R1)

Notes: Award (R1) if either condition is given.

Sufficient to indicate that is ‘within the data range’ and the correlation is ‘strong’.

Allow close to .

Do not accept “within the range of prices”.

[1 mark]

Examiners report














16h. [2 marks]

Markscheme

41

(M1)

Note: Award (M1) for correct substitution into formula.

(A1)(ft)(G2)

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

Accept either the rounded or unrounded answer to part (f).

If no integer value seen in part (f), follow through from their unrounded answer to part (f).

Answer must be positive.

[2 marks]

Examiners report














17a. [1 mark]

Markscheme42

42 kg (A1) (C1)

Note: The units are required.

Examiners report

Many candidates omitted the “kg” units that were required for the median weight. It is not only area

and volume answers where marks may be lost for either missing or incorrect units. Candidates

confused IQR with range. Only the very strongest candidates were able to deduce from a box and

whisker plot that the data was asymmetric (with a positive skew) hence the mean was greater than the

median. This was one of two reasoning marks in the paper and only the very strongest candidates

wrote down a correct reason.

17b. [2 marks]

Markscheme

58 − 33 (A1)

Note: Award (A1) for correct maximum and minimum seen.

= 25 (A1) (C2)

Examiners report







17c. [1 mark]

Markscheme

(A1) (C1)

43

Examiners report







17d. [2 marks]

Markscheme

Mean weight is more than the median weight. (A1)

The upper half of the distribution is wider (more dispersed) or data is positively (or right) skewed or

equivalent reason. (R1)

OR

(R1) (C2)

Note: Do not award (A1)(R0).

Examiners report







Printed for International School of Europe

44

© International Baccalaureate Organization 2019

International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

45

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