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01 Hours 30 Minutes

100 Marks

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IB MATH AI SL, Paper 2, May, 2022, TZ2, Solved Past Paper

Master the 2022 IB May for Paper 2 Mathematics AI SL with examiner tailored solutions and comments for TZ2

Question 1 [Explained]

Mackenzie conducted an experiment to measure the reaction times of teenagers. The results of this experiment are depicted in a cumulative frequency graph, which provides a visual representation of the cumulative number of teenagers corresponding to various reaction times. This graph can be used to estimate statistical measures such as the median, interquartile range, and percentiles of the reaction times.

A cumulative frequency graph showing the reaction times of teenagers.

Question 1 [a] [Explanation]

Utilize the cumulative frequency graph to estimate the following statistical measures:

Question 1 [a] [i] [Explanation]

Estimate the median reaction time using the cumulative frequency graph. The median is the value that separates the higher half from the lower half of the data set. In the context of the cumulative frequency graph, it is the reaction time corresponding to the cumulative frequency that is half of the total number of observations.

Question 1 [a] [ii] [Explanation]

Estimate the interquartile range (IQR) of the reaction times using the cumulative frequency graph. The IQR is the difference between the upper quartile (Q3) and the lower quartile (Q1), representing the range within which the central 50% of the data lies.

Question 1 [b] [Explanation]

Determine the estimated number of teenagers who have a reaction time greater than 0.4 seconds using the cumulative frequency graph.

Question 1 [c] [Explanation]

Determine the 90th percentile of the reaction times from the cumulative frequency graph. The 90th percentile is the reaction time below which 90% of the data falls.

Question 1 [d] [Explanation]

Mackenzie used the following grouped frequency table to create the cumulative frequency graph:

Reaction time, $\boldsymbol t (s)$	Frequency
\(0	3
\(0.2	$a$
\(0.4	13
\(0.6	14
\(0.8	$b$

Question 1 [d] [i] [Explanation]

Identify the value of $a$ from the grouped frequency table.