IB Maths AA SL AA 4.1 Data and descriptive statistics questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
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Question 1

Paper 2, calculatorMedium6 marks

The waiting times, in minutes, for a sample of eight customers at a repair desk were

12, 14, 14, 16, 18, 19, 21, 26.

(a)

Use your GDC to determine the sample mean and sample standard deviation, correct to three significant figures.

[2]
(b)

Hence find the sample variance, correct to three significant figures.

[1]
(c)

For a later report, 3 minutes is subtracted from every waiting time in the sample. A supervisor claims that the standard deviation will therefore also decrease by 3 minutes.

Determine the new sample mean and standard deviation, and comment on the supervisor’s claim.

[3]

Question 2

Paper 1, no calculatorMedium6 marks

A courier company records the delivery times for 40 trips on each of two routes. Figure 1 shows box-and-whisker diagrams for the two sets of times. For this comparison, use the median to represent typical delivery time and the interquartile range (IQR) to represent consistency.

0510152025303540Route BRoute ADelivery time (minutes)
(a)

State the median delivery time for each route.

[2]
(b)

Calculate the IQR for each route.

[2]
(c)

Recommend a route if the company wants both a shorter typical delivery time and more consistent delivery times. Justify your recommendation using the medians and IQRs.

[2]

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