Cambridge International Examinations
General CertiÞcate of Education Ordinary Level
STATISTICS 4040/01
Paper 1 For Examination from 2018
SPECIMEN MARK SCHEME
2 hours 15 minutes
MAXIMUM MARK: 100
This document consists of 6 printed pages.
© UCLES 2015 [Turn over
4040/01 Cambridge O Level – Mark Scheme For Examination
SPECIMEN from 2018
MARK SCHEME NOTES
The following notes are intended to aid interpretation of mark schemes in general, but individual mark
schemes may include marks awarded for specific reasons outside the scope of these notes.
Types of mark
M Method marks, awarded for a valid method applied to the problem.
A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For
accuracy marks to be given, the associated Method mark must be earned or implied.
B Mark for a correct result or statement independent of Method marks.
When a part of a question has two or more ‘method’ steps, the M marks are in principle independent
unless the scheme specifically says otherwise; and similarly where there are several B marks
allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an
earlier, asterisked, mark in the scheme.
The notation ‘ft’ implies that the A or B mark indicated is allowed for work correctly following on from
previously incorrect results. Otherwise, A and B marks are given for correct work only.
Abbreviations
AG answer given on question paper
awrt answer which rounds to
cao correct answer only
dep dependent
ft follow through after error
oe or equivalent
SC special case
soi seen or implied
www without wrong working
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4040/01 Cambridge O Level – Mark Scheme For Examination
SPECIMEN from 2018
Question Answer Marks
1(a) mode B1
1(b) range B1
1(c) median B1
1(d) standard deviation B1
Question Answer Marks
2(a)(i) quota B1
2(a)(ii) systematic B1
2(b) employment status B1
because working women may need to be at work in the afternoon B1
[any other reasonable data item/reason B1/B1, e.g. whether or not a woman
has any children/because a woman with children may prefer to attend in the
afternoon when the children are at school]
Question Answer Marks
3(a) 25 B1
3(b) actors who have worked in LA and R but not M B1
3(c) correct method for number of actors (13 + 5 + 3 + 4 + 9 + 6) M1
40/48 oe A1
3(d) 4/9 B1
Question Answer Marks
4(a) 6 B1
4(b) (6 + 0 + 8 + 2 + 1 + 6 + 0 + 9 + 6 + 4 + 1)/11 (= 43/11) M1
3.9 A1
4(c) ordering of data M1
4 A1
4(d) 3 ft B1
Question Answer Marks
5(a) as the value of one of the variables increases, the value of the other also B1
increases
5(b) positive and strong B1
negative and weak B1
5(c) any diagram with positive correlation B1
diagram with less than perfect positive correlation B1
5(d) appropriate use of positive/negative and strong/weak for their diagram in (c) B1
ft
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4040/01 Cambridge O Level – Mark Scheme For Examination
SPECIMEN from 2018
Question Answer Marks
6(a) (70 – 55)/100 × 80 M1
$12 million A1
6(b) (35/100) × 360 M1
126° A1
6(c) any use of squares of radii M1
correct use of squares of radii M1
3.5 cm A1
Question Answer Marks
7(a) at least two of 15, 22 and 17 B1
54 B1
7(b) any appreciation of area being proportional to frequency M1
(can be earned here or in (c))
6 A1
7(c) rectangle in correct position with height 5 A1
7(d) modal class B1
7(e) product of two probabilities with denominators 70 and 69 B1
3540/4830 oe B1
Question Answer Marks
8(a) attempted use of class mid-points (3.0 3.3 3.5 3.7 3.9 4.1 4.4) * M1
correct method for mean dep M1
accurate expression for mean (∑fx = 139.1 ∑f = 38) A1
3.66 A1
finding values of f × variable squared M1
correct method for SD or variance dep M1
correct expression for SD or variance A1
(∑fx2 = 513.65 mean = 3.66 or better or 3.6 or 3.7)
0.343 A1
8(b)(i) Q B1
8(b)(ii) T B1
8(c) 38 × 3.70 (= 140.6) M1
180 – their 140.6 (= 39.4) M1
their 39.4/180 M1
0.219 or 0.22 A1
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4040/01 Cambridge O Level – Mark Scheme For Examination
SPECIMEN from 2018
Question Answer Marks
9(a) any one age group rate multiplied by standard population figure M1
sum of four such products M1
(50 × 0.18) + (184 × 0.22) + (136 × 0.25) + (15 × 0.35) A1
88.7 A1
9(b) correct method for any age group M1
145 828 714 87 A1
9(c) their values from (b) added (= 1774) M1
2900 + 4500 + 5250 + 5800 (= 18450) M1
(their 1774/their 18450) × 1000 M1
96.2 A1
9(d) 7.8 used anywhere and 8.5 not used M1
their 18450 × 2 M1
× 7.8/1000 or × 8.5/1000 M1
their births – their deaths (= 1774 – 288) M1
1486 A1
Question Answer Marks
10(a) 8 33 85 166 245 313 350 365 B2
(allow B1 follow through for one error)
10(b) correct horizontal plots * M1
correct vertical plots * M1
suitable curve dep A1
(earned provided at least one M scored)
10(c)(i) 21 °C B1
10(c)(ii) Q1 = 15.1 °C – 15.5 °C B1
Q3 = 26.5 °C – 27.0 °C B1
use of IQR = Q3 reading – Q1 reading M1
11 °C – 11.9 °C A1
10(d)(i) 2 °C B1
their (c)(i) + 2 °C ft B1
10(d)(ii) their (c)(ii) ft B1
10(e) attempt to read cf value for T = 34 °C (≈ 345) and subtract from 365 M1
20 ft A1
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4040/01 Cambridge O Level – Mark Scheme For Examination
SPECIMEN from 2018
Question Answer Marks
11(a) correctly plotted points B2
(allow B1 for 6 or 7 correct)
11(b) indication of need to order x values M1
(927 + 1085 + 1219 + 1361)/4 A1
11(c) correct method for LSA M1
(559.75, 25.75) A1
11(d) correct method for gradient using any pair of averages M1
m = 0.0280 or 0.028 A1
c = 10.0 to 10.1 B1
11(e) it indicates the number of teachers required for a school with zero pupils B1
11(f) reasonable line through seven points with a clear outlier above their line B1
11(g) correct method for gradient using points chosen from line M1
m = 0.035 to 0.038 A1
their intercept correct to nearest integer ft B1
11(h) any indication of recognition that m is related to pupil-teacher or teacher-pupil M1
ratio
Belport because there are more teachers per pupil oe A1
so pupils receive more individual attention ft
(or possibly Astra because there are fewer teachers per pupil oe
so more opportunities for individual learning ft)
choice consistent with reason
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