Standard +0.8 This question requires students to work backwards from summary statistics (mean and standard deviation) to deduce individual data values, involving algebraic manipulation of the mean formula and understanding how values affect standard deviation. It goes beyond routine calculation to require problem-solving insight about which value could be removed to simultaneously increase mean and decrease standard deviation.
Alison selects 10 of her male friends. For each one she measures the distance between his eyes. The distances, measured in mm, are as follows:
51 57 58 59 61 64 64 65 67 68
The mean of these data is 61.4. The sample standard deviation is 5.232, correct to 3 decimal places.
One of the friends decides he does not want his measurement to be used. Alison replaces his measurement with the measurement from another male friend. This increases the mean to 62.0 and reduces the standard deviation.
Give a possible value for the measurement which has been removed and find the measurement which has replaced it. [3]
New value is closer to 62 than the old value is to
61.4
e
51 changes to 57
or 57 changes to 63
Answer
Marks
or 58 changes to 64
M1
c
M1
A1
Answer
Marks
[3]
m
i3.1b
2.2a
Answer
Marks
2.2a
Implied by correct answer or pair of
values differing by 6
Implied by correct answer or new
value closer to 62 than old value
Answer
Marks
Guidance
8
0
2
9 a
1
1
9 b
0
2
Question 8:
8 | Increases a value by 6
New value is closer to 62 than the old value is to
61.4
e
51 changes to 57
or 57 changes to 63
or 58 changes to 64 | M1
c
M1
A1
[3] | m
i3.1b
2.2a
2.2a | Implied by correct answer or pair of
values differing by 6
Implied by correct answer or new
value closer to 62 than old value
8 | 0 | 2 | 1 | 0 | 3 | 0
9 a | 1 | 1 | 0 | 0 | 2 | 0
9 b | 0 | 2 | 0 | 0 | 2 | 0
Alison selects 10 of her male friends. For each one she measures the distance between his eyes. The distances, measured in mm, are as follows:
51 57 58 59 61 64 64 65 67 68
The mean of these data is 61.4. The sample standard deviation is 5.232, correct to 3 decimal places.
One of the friends decides he does not want his measurement to be used. Alison replaces his measurement with the measurement from another male friend. This increases the mean to 62.0 and reduces the standard deviation.
Give a possible value for the measurement which has been removed and find the measurement which has replaced it. [3]
\hfill \mbox{\textit{OCR MEI Paper 2 Q8 [3]}}