Mathematics · Oct / Nov 2025 · Paper 61 · Question 5
YMA01
As printed in the paper
The question as text
5. The weights, x grams, of 300 medium-sized apples are summarised in the table below. Weight Frequency 105 x < 115 28 115 x < 125 42 125 x < 130 75 130 x < 140 63 140 x < 150 52 150 x < 170 40 A histogram is drawn (not shown) to represent these data. The bar that represents the class 125 x < 130 is 1.8 cm wide and 12 cm high.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
5(a)[3]
Width = 7.2
Area of 21.6 for a frequency of 75 so 21.6
75 ×
40
=
11.52
for
a frequency of 40 or w × h = 11.52 or fd = 15
11.52
2
=
×
=
h
or
12
1.6
7.2
15
5
5.5
[Q
=
130 ]
+
×
10
or
[Q
=
130 ]
+
×
10
2
63
2
63
5(b)[2]
x −
130
150 145
−
or 140
−
x
208 150
−
or
=
=
−
−
−
−
140 130
208 145
140 130
208 145
= awrt 130.8 or awrt 130.9
]6000[
[
and [
]2 "20" 200
5(c)(i)[2]
y =
=
20]
w =
×
+
300
=
240
150000
[
]
5(c)(ii)[3]
Var( )
y =
−
"20" [ 100]
2
=
300
[
]
w =
×
=
Var( )
4 "100"
400
Notes
(a)
B1
7.2 or exact equivalent
for sight of 11.52 or w × h = 11.52 or fd = 15
M1
May be implied by h = 1.6
A1
1.6 or exact equivalent
for any valid method to find the median allow use of n + 1
(b)
M1
allow working backwards [140 – ] 58 10
or [140 –] 57.5 10
63×
A1
awrt 130.8 allow awrt 130.9 if using (n + 1) No fractions
for a correct method to find the mean of w
(c)(i)
M1
"72000"
Alt:
w =
6000 2 300 200[ 72000]
×+
×
=
and
w =
300
A1
cao correct answer is 2/2
for a correct method to find Var(y)
(c)(ii)
M1
or for
2
w =
17400000
for a correct method to find Var(w) ft their Var(y)
×
+
=
is M0A0
2 "100" 200
400
M1
17400000
or for
w =
−
Var( )
"240"
2
300
A1
cao answer only with no working shown scores M1M0A0
SC
If no marks scored in (ii), allow M1(M0A0) for
150000
−
"20"
2
300
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