Mathematics · Oct / Nov 2024 · Paper 61 · Question 1
YMA01
As printed in the paper
The question as text
1. The back-to-back stem and leaf diagram on page 3 shows information about the running times of 31 Action films and 31 Comedy films. The running times are given to the nearest minute.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[1]
[Mode =] 137
a = 106
1(b)[3]
b = 129
c = 126
4016
(c) (i)
mean =
=
129.5
31
525056
4016
31 525056
4016
2
2
[Standard deviation =]
'
'
or
'
'
(ii)
−
−
31
31
30
31
31
=
12.4
or 12.6
'129.5' '137'
−
[
]
1(c)[3]
[Mode =] 137
a = 106
b = 129
c = 126
4016
(c) (i)
mean =
=
129.5
31
525056
4016
31 525056
4016
2
2
[Standard deviation =]
'
'
or
'
'
(ii)
−
−
31
31
30
31
31
=
12.4
or 12.6
'129.5' '137'
−
[
]
= −
0.6
'12.4'
Negative [skew]
A correct difference of the average or a correct difference of the spread
e.g. On average action films run for longer than comedy films as the median is
greater 129 > 117
Notes
(a)
B1
Cao Must be seen in part (a)
(b)
B1
a = 106 Must be attached to a (Condone
Q /lower quartile for a)
1
B1
b = 129 Must be attached to b (Condone
Q /median for b)
2
B1
c = 126 Must be attached to c (Condone
Q /upper quartile for c)
3
(c) (i)
B1
awrt 130
For a correct method (including the square root) to find the standard deviation. Ft their mean
(ii)
M1
May be implied by awrt 12.4 or awrt 12.9 or awrt 12.6 if sample standard deviation is calculated
A1
awrt 12.4 or awrt 12.6 if sample standard deviation is calculated Correct answer only scores 2/2
For substitution of the mode, the mean and the standard deviation into the expression. Ft their
(d)
M1
mode, their mean and their standard deviation. Allow awrt −0.6 if no working shown.
A1ft
A correct interpretation ft their expression. Ignore any reference to correlation
for a correct comment, referring to length, with reference to a correctly named statistic. Must
(e)
B1ft
include the correct figures compared. Ft their values. Ignore any reference to skew
The following table may be useful (but not an exhaustive list of possible answers)
Statistic
A
C
Comment
Median
129
117
On average action films run for longer as the median is greater 129 > 117
Mean
129.5 114.5 On average action films have a greater running time as the mean is greater 129.5 > 114.5
Mode
137
127
On average comedy films are shorter in length as the mode is less 127 < 137
IQR
17
20
Comedy films have a greater spread of running times as the IQR is greater 20 > 17
Range
57
39
Action films have a larger variation of running times as the range is greater 57 > 39
SD
12.4
11.9
Comedy films show less variability in the length of films as the SD is less 11.9 < 12.4
2015
2
[
]
1(d)[2]
= −
0.6
'12.4'
Negative [skew]
A correct difference of the average or a correct difference of the spread
1(e)[1]
e.g. On average action films run for longer than comedy films as the median is
greater 129 > 117
Notes
(a)
B1
Cao Must be seen in part (a)
(b)
B1
a = 106 Must be attached to a (Condone
Q /lower quartile for a)
1
B1
b = 129 Must be attached to b (Condone
Q /median for b)
2
B1
c = 126 Must be attached to c (Condone
Q /upper quartile for c)
3
(c) (i)
B1
awrt 130
For a correct method (including the square root) to find the standard deviation. Ft their mean
(ii)
M1
May be implied by awrt 12.4 or awrt 12.9 or awrt 12.6 if sample standard deviation is calculated
A1
awrt 12.4 or awrt 12.6 if sample standard deviation is calculated Correct answer only scores 2/2
For substitution of the mode, the mean and the standard deviation into the expression. Ft their
(d)
M1
mode, their mean and their standard deviation. Allow awrt −0.6 if no working shown.
A1ft
A correct interpretation ft their expression. Ignore any reference to correlation
for a correct comment, referring to length, with reference to a correctly named statistic. Must
(e)
B1ft
include the correct figures compared. Ft their values. Ignore any reference to skew
The following table may be useful (but not an exhaustive list of possible answers)
Statistic
A
C
Comment
Median
129
117
On average action films run for longer as the median is greater 129 > 117
Mean
129.5 114.5 On average action films have a greater running time as the mean is greater 129.5 > 114.5
Mode
137
127
On average comedy films are shorter in length as the mode is less 127 < 137
IQR
17
20
Comedy films have a greater spread of running times as the IQR is greater 20 > 17
Range
57
39
Action films have a larger variation of running times as the range is greater 57 > 39
SD
12.4
11.9
Comedy films show less variability in the length of films as the SD is less 11.9 < 12.4
2015
2
[
]
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