Mathematics · May / June 2022 · Paper 61 · Question 3
YMA01
As printed in the paper
The question as text
3. Gill buys a bag of logs to use in her stove. The lengths, l cm, of the 88 logs in the bag are summarised in the table below. Length (l) Frequency ( f ) 15 < l 20 19 20 < l 25 35 25 < l 27 16 27 < l 30 15 30 < l 40 3 A histogram is drawn to represent these data. The bar representing logs with length 27 < l 30 has a width of 1.5 cm and a height of 4 cm.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[3]
Width = 2.5 (cm)
or 4
Height = 35
×
6
÷
"2.5"
5 ×
7
or 6cm2 = 15 (logs) or 14cm2 = 35 (logs) oe
15
= 5.6 (cm)
25
25.5
Median [
]
allow [
]
=
20
+
×
5
20
+
×
5
3(b)[2]
35
35
= 23.57… allow 23.64….
awrt 23.6 A1
3(c)[1]
19 + 35 + 8 (= 62*) or 88 – 3 – 15 – 8 (= 62*)
B1cso*
P(4 logs fit) = 62
61
60
59
3(d)[2]
×
×
×
M1
88
87
86
85
= 0.23922….
awrt 0.239 A1
924
[
]
3(e)(i)[3]
mean of
y =
=
10.5
M1
88
mean of
(
"10.5" 255
)
2
w =
+
×
M1
= 531
A1
12862
(
) [
2
]
3(e)(ii)[3]
variance of
y =
−
"10.5"
=
35.909...
M1
88
variance of
"35.909" 4
w =
×
or
"35.909" 0.5
÷
2
M1
= 143.636…
awrt 144 A1
Notes
(a)
B1
2.5 oe
Correct method to relate area to number of logs (may be implied by “their w” × “their h” = 14)
M1
5.6 oe
A1
(b)
10
For a correct fraction multiplied by 5. Allow working downwards e.g. [
]
25
5
M1
−
×
35
Correct answer from correct working. Allow exact fraction.
A1
(c)
2 (16) for 8. Allow equivalent methods
54
=
26 25
A correct calculation seen. Allow 1
x−
−
70 54
−
27 25
−
B1
NB: 26 + x = 88→ x = 62 is B0.
Minimum working required 54 + 8 or 70 – 8 or 54 70
+
2
(d)
n
n
−
1
n
−
2
n
−
3
For
×
×
×
(allow any n < 88)
M1
88
87
86
85
A1
awrt 0.239
SC
With replacement awrt 0.246 scores M1A0
(e)(i)
Correct method for finding mean of y (implied by 10.5) or for equation0.5
w−
88 255
×
M1
and 46728
46728
Correct method for finding mean of w or
w =
M1
88
Cao
A1
(ii)
Correct method for finding variance of y (implied by awrt 35.9)
M1
0.25
2
255
2
88
255
12862
or
w
+
×
−
w
=
24825208
Correct method for finding variance of w or
w =
2
24825208
and
−
"531"
2
M1
88
P(
∪
)
=
P(
)
+
P(
)
−
P(
∩
)
P(
'
∩
)
=
P(
∪
)
−
P(
)
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