Mathematics · May / June 2022 · Paper 61 · Question 1
YMA01
As printed in the paper
The question as text
1. The company Seafield requires contractors to record the number of hours they work each week. A random sample of 38 weeks is taken and the number of hours worked per week by contractor Kiana is summarised in the stem and leaf diagram below. Stem Leaf Key : 3 2 means 32 1 4 4 4 5 5 5 6 6 9 9 9 (11) 2 1 2 2 3 3 4 4 4 w 9 (10) 3 2 3 4 4 5 6 7 7 7 9 (10) 4 1 1 2 3 (4) 5 1 9 (2) 6 4 (1) The quartiles for this distribution are summarised in the table below. x 26 y
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[3]
w = 8
x = 19
y = 37
"37" 1
(
"37" "19"
)
1(b)[2]
+ ×
−
[= 55]
59 and 64
1(c)[3]
(
) (
)
"37" 26
−
−
26
−
"19"
1(d)[2]
M1
(
)
"37" "19"
−
= 0.22 (to 2 sf)
A1
1(e)[1]
E.g. ‘The mean uses all the data’
B1
Notes
(a)
B1B1B1 Cao May be seen in table before part (a). w = 28 is first B0.
(b)
Calculation for the outliers using their lower quartile and upper quartile.
M1
Allow “their upper quartile” + “their IQR” for this mark i.e. 37 + 18
For identifying 59 and 64 as outliers from correct working.
Ft the identification of outlier(s) (if any) from “their 55” from their shown calculation.
A1ft
Answer only is M0A0.
(c)
M1
For a box with at least one whisker drawn
14 for lowest whisker, 26 for median, "19" and "37" plotted for quartiles ft their values for
A1ft
quartiles
Upper whisker at 51 or “their 51” plus "their outliers” plotted but there must be at least one outlier
for this mark. Condone upper whisker at "their 55".
A1ft
NB award A0 if there is more than one whisker at either end
(d)
M1
For substituting their values into the formula
Allow awrt 0.22 (allow 2
or 0.2
)
A1
9
(e)
A correct reason which supports Landacre’s use of the mean or rejects their use of the median.
Allow comment relating to (slight) positive skew so mean > median so Landacre will know the
larger average they will have to pay.
Comments about skewness/symmetry on their own score B0.
B1
Mean includes the outliers is B1.
Condone Median is not affected by the outliers for B1.
Mean is more accurate is B0.
144.84
2
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