# Exam-Style Question on Statistics

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 206. This question is similar to one that appeared on an IB Studies paper in 2015. The use of a calculator is allowed.

This cumulative frequency graph shows the speeds in kmh-1 of cyclists passing a certain point on a race track.

(a) Estimate the minimum possible speed of one of these cyclists.

(b) Find the median speed of the cyclists.

(c) Write down the 65th percentile.

(d) Calculate the interquartile range.

(e) Find the number of these cyclists that were travelling faster than 22 kmh-1

The table shows the speeds of these cyclists.

Speed of Cyclists (s)Number of Cyclists
$$0 \lt s \le 5$$0
$$5 \lt s \le 10$$$$a$$
$$10 \lt s \le 15$$8
$$15 \lt s \le 20$$20
$$20 \lt s \le 25$$16
$$25 \lt s \le 30$$5
$$30 \lt s \le 35$$$$b$$

(f) Find the value of $$a$$ and of $$b$$

(g) Write down the modal class.

(h) Write down the mid-interval value for the modal class.

(i) Use your graphic display calculator to calculate an estimate of the mean speed of these cyclists.

(j) Use your graphic display calculator to calculate an estimate of the standard deviation of the speeds of these cyclists.

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