Mathematics · May / June 2022 · Paper 61 · Question 2
YMA01
As printed in the paper
The question as text
2. Stuart is investigating the relationship between Gross Domestic Product (GDP) and the size of the population for a particular country. He takes a random sample of 9 years and records the size of the population, t millions, and the GDP, g billion dollars for each of these years. The data are summarised as n = 9 ∑ t = 7.87 ∑ g = 144.84 ∑ g2 = 3624.41 Stt = 1.29 Stg = 40.25
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2(a)[3]
S
gg =
3624.41
−
=
1293.4516
9
40.25
r =
"1293.4516" 1.29
×
= 0.985….
awrt 0.985 A1
2(b)[1]
As the population/t increases, GDP/g increases oe
40.25
[
]
2(c)[4]
b =
=
31.20155...
M1
1.29
144.84
7.87
[
]
a =
−
"31.20155..."
×
= −
11.19068....
M1
9
9
g
=
...31.20155...
t
A1
= −
11.2
+
31.2
g
t
A1
The GDP/g increases by (an average of) "31.2" billion [dollars] when the population/t
2(d)[1]
increases by one million.
2(e)(i)[2]
" 11.2" "31.2" 7
−
+
×
M1
= 207.2…
awrt 207 A1
2(e)(ii)[1]
Unreliable as 7 000 000 is much greater than the mean population/ t for the 9 years.
2(f)[2]
0.1
=
"31.2"x
M1
x =
0.003205...
million people
awrt 0.0032 A1
Notes
(a)
Correct method for finding Sgg (implied by awrt 1290 to 3sf)
M1
M1
Correct method for finding r using their Sgg If Sgg = 3624.41 is used here, then M0.
awrt 0.985 (correct answer only scores M1M1A1)
A1
(b)
A correct interpreted contextual statement including population (or t) and GDP (or g).
B1
‘Strong positive correlation between population and GDP’ on its own is B0.
(c)
Correct method for finding b
M1
Correct method for finding a using their b
M1
[
]
a =
16.0... "31.20155..." 0.874...
−
×
= −
11.19068....
Only dep on 1st M1 awrt 31.2 in a regression equation (allow any variables in the equation).
A1
Correct equation
g
=
awrt
−
11.2
+
awrt 31.2
t
(must be g and t) Do not allow fractions.
A1
(d)
Idea that the GDP increases by “Their b” billion dollars for every 1 million increase in population
B1
(e)(i)
Correct method. Allow substitution of 7 000 000 instead of 7
M1
A1
awrt 207 (billion) (isw after an answer of 207 is seen)
(ii)
Unreliable with a correct supporting comment which must reference t or t [=0.874] or population
B1
‘Extrapolation so unreliable’ on its own is B0. Reference to g out of range is also B0.
(f)
Equating 0.1 with “their b” × x
M1
Or substituting two values for g with a difference of 0.1 in their equation leading to a value of x
awrt 0.0032 (million) Allow awrt 3200 (to 2sf) Do not allow fractions.
A1
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