Mathematics · May / June 2023 · Paper 61 · Question 3
YMA01
As printed in the paper
The question as text
3. Jim records the length, l mm, of 81 salmon. The data are coded using x = l – 600 and the following summary statistics are obtained. n = 81 ∑x = 3711 ∑x 2 = 475 181
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[3]
=
3711 81 600
+
×
=
52311
[
]
[
]
l
x =
=
45.814...
81
"52311"
l
=
"45.814..." 600
+
l
=
81
l
=
645.81...
awrt 646
3(b)[2]
475181
3711
2
2
34088381
"52311"
[
]
[
]
2
=
−
=
3767
Var( )
L
=
−
x
81
81
81
81
=
3767.43...
l
2
=
3767.43...
= 3767.43… awrt 3770
40
3(c)[1]
The answer is a drawing: see the picture of this mark scheme row.
3(d)[3]
IQR = 5400 – 3800 [= 1600]
5400 1.5 "1600"
+
×
[= 7800] or3800 1.5 "1600"
−
×
[= 1400]
7800 > 7700 and 1400 < 1600 therefore there are no outliers
Notes
(a)
Allow 45.8 or better. Ignore labels
M1 for a correct method to find x or
l
M1 for a correct method to find l ft their x if it is clearly labelled or it comes from 3711
81
if it is clearly labelled or comes from 3711 81 600
+
×
their
l
A1 awrt 646 or 17437
or 52311
oe
27
81
M1 correct method to find Var (X) implied by awrt 3770 or a correct method to find Var (L) ft their
(b)
or Allow calculation of sd[
]
=
awrt 61.4
Ignore labels
l
x
A1 awrt 3770 labelled clearly as Var(L) or Var (L) = Var(X) or
=
stated or variance is not
l
x
34088381
"52311"
changed by coding is stated or they have gained the answer from
−
81
81
B1 cao
(c)
M1 correct method to find IQR. May be implied by a correct limit.
(d)
NB 1.5 (5400
×
−
3800)
=
2400
M1 for a correct method to find the upper or the lower outlier boundary.
A1 both 7800 and 1400 correct and 7700 and 1600 (as the minimum not IQR) seen and explicitly
stating no outliers
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