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![Page 1: misswelton.weebly.com · Web viewMost candidates could state whether the data was discrete or continuous and find the mode however the calculations to find the mean, median and …](https://reader036.vdocuments.site/reader036/viewer/2022070811/5f09c6447e708231d4287062/html5/thumbnails/1.jpg)
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
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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
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= 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
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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
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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
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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
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[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
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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
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(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
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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
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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
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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
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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)
Note: Accept an answer in the range 10000 to 10250.
[1 mark]
Examiners report
[N/A]
7d. [1 mark]
Markscheme
16000 (G1)
Note: Accept an answer in the range 16000 to 16250.
[1 mark]
Examiners report
[N/A]
7e. [1 mark]
13
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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
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[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
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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
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[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
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[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
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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
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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
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[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
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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
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[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
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(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
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(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
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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
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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
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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
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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 .
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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]
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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)
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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.
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(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
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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.
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
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.
16a. [4 marks]
Markscheme
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(A4)
Notes: Award (A1) for correct scale and labels (accept and ).
Award (A3) for or points plotted correctly.
Award (A2) for or points plotted correctly.
Award (A1) for or points plotted correctly.
Award at most (A1)(A2) if points are joined up.
If axes are reversed, award at most (A0)(A3).
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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
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
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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).
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
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).
16d. [3 marks]
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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
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).
16e. [2 marks] 38
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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
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).
16f. [3 marks]
Markscheme
(M1)
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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
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
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frequently seen. Percentage error caused very few problems for candidates and many correct answers
were seen in part (h).
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
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).
16h. [2 marks]
Markscheme
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(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
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).
17a. [1 mark]
Markscheme42
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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
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.
17c. [1 mark]
Markscheme
(A1) (C1)
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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.
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
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.
Printed for International School of Europe
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© International Baccalaureate Organization 2019
International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®
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