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 1 Paper 2

Difficulty

Easy Medium Hard

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.

(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.

Route	Lower whisker end	Lower quartile	Median	Upper quartile	Upper whisker end
A	12	18	24	30	36
B	10	15	20	28	40

(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]

Question 4

Paper 2Medium6 marks

Ridgeway College wants to estimate the usual one-way travel time of all its students. A staff member asks the first 40 students they meet as they leave the cafeteria at lunch. For these responses, the lower quartile is 18 minutes and the upper quartile is 30 minutes. One recorded travel time is 55 minutes.

(a)

Calculate the interquartile range (IQR).

[1]

(b)

Determine whether the travel time of 55 minutes is an outlier. Show a comparison with the nearest quartile.

[2]

(c)

The student confirms that 55 minutes is accurate for their usual journey, which includes a ferry crossing and a transfer. Should this value be removed when summarizing the sample? Justify your answer.

[1]

(d)

Explain one limitation of the staff member’s sampling method and suggest a more suitable sampling method.

[2]

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