Mathematics · May / June 2024 · Paper 61 · Question 1
YMA01
As printed in the paper
The question as text
1. A researcher is investigating the growth of two types of tree, Birch and Maple. The height, to the nearest cm, a seedling grows in one year is recorded for 35 Birch trees and 32 Maple trees. The results are summarised in the back‑to‑back stem and leaf diagram below. Totals Birch Maple Totals (2) 9 8 2 5 7 7 8 9 (5) (8) 9 9 9 6 5 3 1 1 3 0 2 6 6 8 9 9 (7) (9) 9 8 8 7 6 3 1 1 1 4 1 1 1 k 7 8 (6) (9) 7 7 7 5 4 3 2 1 0 5 0 1 2 3 4 4 4 (7) (3) 7 6 5 6 3 4 6 (3) (3) 6 5 4 7 0 7 (2) (1) 5 8 0 0 (2) Key: 5 | 6 | 3 means 65 cm for a Birch tree and 63 cm for a Maple tree The median height that these Maple trees grow in one year is 45 cm.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[1]
k = 3
39
57
1(b)[2]
Q =
Q =
1
3
(
)
(
)
1(c)[2]
"57" 1.5
+
×
"57" "39"
−
or
"39" 1.5
−
×
"57" "39"
−
84 and 12 therefore only 1 outlier [85]
1(d)[4]
A correct difference of the medians with supporting figures
e.g. On average Birch [trees grow slightly] taller as the median is
larger 48 > 45 oe
or
1(e)[1]
A correct difference of the spread with supporting figures
e.g. Maple has a greater spread/variation of heights as the range is
larger 55 > 48 (excluding outlier) oe
e.g. Birch has a greater spread/variation of heights as the range is
larger 57 > 55 (with outlier) oe
1(f)[3]
36
„
<
where 43
„
„
45
or 54
„
2
„
80
a
x
x
a
36
„
a
„
"43"
and 54
„
2
a
„
80
A1ft
36
„
„
40
A1
a
Notes
(a)
Cao
B1
(b)
B1
for Q1 correct
for Q3 correct
B1
(c)
for either method correct or a correct value (ft their Q1 and their Q3)
M1
A1
Both limits for outliers correct and statement about the outlier or the outlier given.
for a box drawn with only 2 whiskers, only one at each end (condone median line
(d)
M1
missing)
for upper whisker ending at 76 (or 84 ft their upper outlier limit) and lower
M1
whisker ending at 28
for Q1, Q2 and Q3 plotted, with Q2 = 48 and ft their Q1 and Q3
M1
for a fully correct box plot with the outlier correctly shown – must be only 1
A1
for a correct comment, referring to heights, with reference to a correctly named
statistic. Must include the figures compared.
(e)
B1ft
Allow ‘grow more/bigger’ to imply taller
Ignore any reference to skew SC If Q1/Q3 are incorrect then allow a ft
comment about spread referring to the difference in IQR if compared to 18
for either range correct. Allow 72 ⩽ 2a ⩽ 80 or 27 ⩽ a ⩽ 40 for 54
Condone < rather than „
(f)
M1
May be seen as separate inequalities e.g. 2a ⩽ 80, 2a ⩾54 is allowed for
54
„
2
a
„
80
A final answer of 36
„
„
40
or 36
<
<
40
implies M1
a
a
for both ranges correct ft their k. Allow 72 ⩽ 2a ⩽ 80 or 27 ⩽ a ⩽ 40 for
A1ft
54
„
2
„
80
Condone < rather than „ May be seen as separate inequalities
a
Allow 36 to 40 or 36, 37, 38, 39, 40
A1
NB It is possible to get M1A0A1
(
) = 0.45
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