A Level · Mathematics 9709 · Probability & Statistics 1

Representation of data: A Level Mathematics questions with answers

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

Generate a full Representation of Data worksheet →All Probability & Statistics 1 questions

Representation of data practice questions

Question 1Structured · 7 marksA* challenge

The times, x minutes, taken by 13 students to complete a puzzle are summarised by Σx = 728 and Σx2 = 41600. Another 11 students had mean time 66 minutes and standard deviation 5 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 24 students.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)56, 8
mean 56 B1
√(41600 ÷ 13 − 562) = 8 B1
2
(b)60.6, 8.42
Σx for second group = 726 B1
Σx2 for second group = 48191 M1
combined mean 60.6 A1
combined variance formula M1
s.d. 8.42 A1
5
Question 2Structured · 3 marks

For a set of 33 values, Σx = 1085.7 and Σx2 = 35925.8. Find the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
mean 32.9, sd 2.5
32.9 B1
√(Σx2/n − mean2) M1
2.5 A1
3
Question 3Structured · 6 marks

The masses, in grams, of 9 eggs are
16 17 23 23 26 27 31 53 56

(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 26; IQR 22
median 26 B1
quartiles M1
IQR 22 A1
3
(b)30.2; 13.7
mean B1
Σx2/n − mean2 M1
sd A1
3
Question 4Structured · 7 marksA* challenge

The times, x minutes, taken by 30 students to complete a puzzle are summarised by Σx = 1260 and Σx2 = 53670. Another 19 students had mean time 61 minutes and standard deviation 6 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 49 students.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)42, 5
mean 42 B1
√(53670 ÷ 30 − 422) = 5 B1
2
(b)49.4, 10.7
Σx for second group = 1159 B1
Σx2 for second group = 71383 M1
combined mean 49.4 A1
combined variance formula M1
s.d. 10.7 A1
5
Question 5Structured · 3 marks

For a set of 24 values, Σx = 391.2 and Σx2 = 7519.2. Find the mean and standard deviation.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
mean 16.3, sd 6.9
16.3 B1
√(Σx2/n − mean2) M1
6.9 A1
3
Question 6Structured · 6 marks

The masses, in grams, of 9 eggs are
32 33 37 42 43 45 52 56 60

(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 43; IQR 19
median 43 B1
quartiles M1
IQR 19 A1
3
(b)44.4; 9.32
mean B1
Σx2/n − mean2 M1
sd A1
3

More Probability & Statistics 1 questions

Permutations & combinationsProbability & the binomial distributionDiscrete random variablesThe normal distribution

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in