Mathematics · Oct / Nov 2023 · Paper 61 · Question 2

YMA01

As printed in the paper

The question as text

2. The weights, to the nearest kilogram, of a sample of 33 red kangaroos taken in December are summarised in the stem and leaf diagram below. Weight (kg) Totals Key: 3 | 2 represents 32 kg 1 6 (1) 2 3 6 (2) 3 2 4 6 (3) 4 2 5 5 6 6 7 8 (7) 5 3 4 7 7 7 8 9 9 (8) 6 0 2 2 3 3 7 8 (7) 7 2 8 (2) 8 2 6 (2) 9 4 (1)

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2(a)[3]
Q =
57
2
(ii)
Q =
45
Q =
63
1
3
'63' 1.5('63' '45')[ 90]
or '45' 1.5('63' '45')[ 18]
+
−
=
−
−
=
= 90 or = 18
16 and 94 [are outliers]*
A boxplot drawn with 2 whiskers
Q ,
Q and
Q plotted correctly
1
2
3
Whiskers drawn correctly
Outliers marked at 16 and 94
The median/Q2 for February is less/lower than the median/Q2 for December oe
The IQR/range for February is less/lower than December (allow similar) oe
For a correct interpretation of either average or spread
e.g.
on average February weigh less than December oe
the weights of February are less varied/little change in variability than the
weights of December oe
They weighed more later in the year oe
Most of the distribution has shifted right, implying that most kangaroos have
gained weight but some appear to have lost weight.
Notes
(a)(i)
Cao
B1
(ii)
Cao
B1
B1
Cao
(b)
For use of either
Q
+
1.5(
Q
−
Q
)
or
Q
−
1.5(
Q
−
Q
)
ft part (a)
M1
3
3
1
1
3
1
For either 90 or 18 ft part (a)
A1ft
For identifying both outliers with no incorrect/missing working (This can ft part (a))
A1*
(c)
M1
A boxplot drawn with 2 whiskers
For
Q ,
Q and
Q plotted correctly ft part (a)
A1ft
1
2
3
Whiskers drawn at 18 and 90 ft part (b) or 23 and 86
A1ft
Outliers marked at 16 and 94
A1
A correct comparison of medians ft their boxplot drawn or part (a) (No figures are required but if
(d)
B1ft
quoted then they need to be correct ft) Must mention the word median/Q2
A correct comparison of range/IQR ft their boxplot drawn or part (a) (No figures are required but
B1ft
if quoted then they need to be correct ft) Must mention either IQR or range
B1ft
A correct interpretation of either the average or the spread ft their boxplot drawn or part (a)
NB Ignore any reference to skew or outliers
2(b)[3]
+
−
=
−
−
=
= 90 or = 18
16 and 94 [are outliers]*
2(c)[4]
A boxplot drawn with 2 whiskers
Q ,
Q and
Q plotted correctly
1
2
3
Whiskers drawn correctly
Outliers marked at 16 and 94
2(d)[3]
The median/Q2 for February is less/lower than the median/Q2 for December oe
The IQR/range for February is less/lower than December (allow similar) oe
For a correct interpretation of either average or spread
e.g.
on average February weigh less than December oe
the weights of February are less varied/little change in variability than the
weights of December oe
They weighed more later in the year oe
Most of the distribution has shifted right, implying that most kangaroos have
gained weight but some appear to have lost weight.
Notes
(a)(i)
Cao
B1
(ii)
Cao
B1
B1
Cao
(b)
For use of either
Q
+
1.5(
Q
−
Q
)
or
Q
−
1.5(
Q
−
Q
)
ft part (a)
M1
3
3
1
1
3
1
For either 90 or 18 ft part (a)
A1ft
For identifying both outliers with no incorrect/missing working (This can ft part (a))
A1*
(c)
M1
A boxplot drawn with 2 whiskers
For
Q ,
Q and
Q plotted correctly ft part (a)
A1ft
1
2
3
Whiskers drawn at 18 and 90 ft part (b) or 23 and 86
A1ft
Outliers marked at 16 and 94
A1
A correct comparison of medians ft their boxplot drawn or part (a) (No figures are required but if
(d)
B1ft
quoted then they need to be correct ft) Must mention the word median/Q2
A correct comparison of range/IQR ft their boxplot drawn or part (a) (No figures are required but
B1ft
if quoted then they need to be correct ft) Must mention either IQR or range
B1ft
A correct interpretation of either the average or the spread ft their boxplot drawn or part (a)
NB Ignore any reference to skew or outliers

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