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.

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Question 1

Paper 2, calculatorMedium6 marks

A transport planner records journey times, $t$ minutes, for shuttle route Cedar. The cumulative frequency is the number of journeys with a time less than the upper boundary of the class.

Class interval	Cumulative frequency at upper boundary
$0\leq t<5$	1
$5\leq t<10$	4
$10\leq t<15$	9
$15\leq t<20$	19
$20\leq t<25$	31
$25\leq t<30$	38
$30\leq t<35$	40

For estimates between class boundaries, assume the cumulative frequency graph consists of straight line segments and starts at $(0,0)$

(a)

State the total number of journeys recorded for route Cedar.

[1]

(b)

Using a cumulative frequency graph, estimate the median and interquartile range of the journey times for route Cedar. Give your answers to the nearest $0.1$ minute.

[3]

(c)

For route Birch, the lower quartile is $12$ minutes, the median is $18$ minutes and the upper quartile is $24$ minutes.

Hence compare the typical journey time and the spread of journey times for the two routes, using the medians and interquartile ranges.

[2]

Question 2

Paper 1, no calculatorMedium6 marks

The histogram in Figure 1 shows the response times, $x$ seconds, for 32 service calls. The standard deviation of these response times is $6.4$ seconds.

(a)

State the modal class and estimate the mean response time.

[3]

(b)

For each response time $x$ a service index $y$ measured in index units, is defined by

y=2(x-3).

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

[3]

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