AS Level · Mathematics 9709 · Probability & Statistics 1

Representation of data: AS Level Mathematics questions with answers

Free Representation of data questions for AS Level Mathematics (9709), part of Probability & Statistics 1. Each question has the answer and the marking points an examiner would look for.

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Representation of data practice questions

Question 1Structured · 7 marksA* challenge

The times, x minutes, taken by 24 students to complete a puzzle are summarised by Σx = 1176 and Σx2 = 59568. Another 16 students had mean time 46 minutes and standard deviation 8 minutes.

(a)

Find the mean and standard deviation of the times of the first group.

[2]
(b)

Find the mean and standard deviation of the times of all 40 students.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)49, 9
mean 49 B1
√(59568 ÷ 24 − 492) = 9 B1
2
(b)47.8, 8.74
Σx for second group = 736 B1
Σx2 for second group = 34880 M1
combined mean 47.8 A1
combined variance formula M1
s.d. 8.74 A1
5
Question 2Structured · 3 marks

For a set of 31 values, Σx = 775 and Σx2 = 20031. Find the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
mean 25, sd 4.6
25 B1
√(Σx2/n − mean2) M1
4.6 A1
3
Question 3Structured · 6 marks

The masses, in grams, of 9 eggs are
11 16 26 26 30 41 44 45 50

(a)

Find the median and the interquartile range.

[3]
(b)

Calculate the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)median 30; IQR 23.5
median 30 B1
quartiles M1
IQR 23.5 A1
3
(b)32.1; 12.9
mean B1
Σx2/n − mean2 M1
sd A1
3
Question 4Structured · 7 marksA* challenge

The times, x minutes, taken by 16 students to complete a puzzle are summarised by Σx = 1024 and Σx2 = 67136. Another 24 students had mean time 68 minutes and standard deviation 9 minutes.

(a)

Find the mean and standard deviation of the times of the first group.

[2]
(b)

Find the mean and standard deviation of the times of all 40 students.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)64, 10
mean 64 B1
√(67136 ÷ 16 − 642) = 10 B1
2
(b)66.4, 9.61
Σx for second group = 1632 B1
Σx2 for second group = 112920 M1
combined mean 66.4 A1
combined variance formula M1
s.d. 9.61 A1
5
Question 5Structured · 3 marks

For a set of 24 values, Σx = 768 and Σx2 = 25225. Find the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
mean 32, sd 5.2
32 B1
√(Σx2/n − mean2) M1
5.2 A1
3
Question 6Structured · 6 marks

The masses, in grams, of 9 eggs are
12 28 30 34 35 37 42 44 47

(a)

Find the median and the interquartile range.

[3]
(b)

Calculate the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)median 35; IQR 14
median 35 B1
quartiles M1
IQR 14 A1
3
(b)34.3; 9.88
mean B1
Σx2/n − mean2 M1
sd A1
3

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