IB Maths AA HL 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
EasyMediumHard

Question 1

Paper 1, no calculatorEasy6 marks

The table shows the five-number summaries for daily journey times at two depots.

DepotMinimum (min)Lower quartile (min)Median (min)Upper quartile (min)Maximum (min)
A1218243036
B1016222940
(a)

Write down the median journey time for depot A.

[1]
(b)

Calculate the interquartile range for each depot.

[2]
(c)

State which depot has less variation among the middle 50% of journey times.

[1]
(d)

State which depot’s distribution appears more nearly symmetric, giving a feature of its five-number summary to support your answer.

[2]

Question 2

Paper 1, no calculatorMedium6 marks

The histogram in Figure 1 shows the response times, xx seconds, for 32 service calls. The standard deviation of these response times is 6.46.4 seconds.

010203040506002468101214Response time, x (s)Frequency
(a)

State the modal class and estimate the mean response time.

[3]
(b)

For each response time xx a service index yy measured in index units, is defined by

y=2(x−3).y=2(x-3).

Hence, using your estimate from part (a), determine the estimated mean and the standard deviation of yy

[3]

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