Exam-Style Question on Cumulative Frequency

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

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Question id: 581. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

Gringe Hull Secondary School has students from Year 7 to Year 13. A group of 138 students in Year 9 were randomly selected and surveyed to find out how long it takes them to travel to school each morning. Their results are represented by the following cumulative frequency graph.

(a) Find the median number of minutes per day these Year 9 students spend travelling to school.

(b) Given that 20% of these Year 9 students spend more than $$k$$ minutes per day travelling to school, find value of $$k$$.

The same information is represented by the following table.

Travelling time (m) in minutes Frequency
0 < m ? 5 4
5 < m ? 10 10
10 < m ? 15 14
15 < m ? 20 $$p$$
20 < m ? 25 22
25 < m ? 30 21
30 < m ? 35 16
35 < m ? 40 $$q$$
40 < m ? 45 9
45 < m ? 50 6
50 < m ? 55 3
55 < m ? 60 1

(c) Find the value of $$p$$ and the value of $$q$$.

There are 450 students in Year 9 at this school.

(d) Estimate the number of Year 9 students that spend less than 15 minutes travelling to school each day.

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