IB Maths AI SL AI 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 1Paper 2
Difficulty
EasyMediumHard

Question 1

Paper 2Easy6 marks

A city council wants to describe the repair times for 240 potholes repaired during April. It selects 12 repair records at random. For these 12 records, the lower quartile is 4 hours and the upper quartile is 8 hours. One recorded repair time is 18 hours.

(a)

State the population and the sample.

[2]
(b)

Calculate the interquartile range and determine whether the 18-hour repair time is an outlier.

[2]
(c)

The maintenance log confirms that this repair took 18 hours because a lane closure delayed the crew. State whether the value should be removed before describing the sample, giving a reason.

[2]

Question 2

Paper 2Easy5 marks

A school records the commute times of students travelling by two bus routes. Figure 1 shows box-and-whisker diagrams of the times, in minutes.

051015202530354045505560Route BRoute ACommute time (minutes)
(a)

Write down the median commute time for Route A.

[1]
(b)

Calculate the interquartile range of the commute times for Route B. Give your answer in minutes.

[2]
(c)

State which route’s commute times may be normally distributed. Give one feature of its box-and-whisker diagram to support your answer.

[2]

Question 3

Paper 2Easy5 marks

A delivery service compares the delivery times for two routes. The values below summarize the box-and-whisker plots for each route. All values are in minutes.

RouteLower whisker endLower quartileMedianUpper quartileUpper whisker end
A1218243036
B1015202840
(a)

Calculate the interquartile range for each route.

[2]
(b)

State which route has the higher median delivery time.

[1]
(c)

State which route’s delivery times may be normally distributed. Give a reason based on the symmetry of its box and whiskers.

[2]

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