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Question id: 108. This question is similar to one that appeared in an IB Studies paper in 2014. The use of a calculator is allowed.

Statistics

The following grouped frequency table shows the length of time, \(t\), in minutes, visitors watched an octopus swimming around a tank at an aquarium.

Time (\(t\))Visitors
\(0\lt t \le 5\)23
\(5\lt t \le 10\)13
\(10\lt t \le 15\)9
\(15\lt t \le 20\)6
\(20\lt t \le 25\)2
\(25\lt t \le 30\)1

(a) Write down the total number of visitors who were included in the survey.

(b) Write down the mid-interval value for the \(20\lt t \le 25\) group.

(c) Find an estimate of the mean time visitors took watching the octopus.

The information above has been rewritten as a cumulative frequency table.

Time (\(t\))\(t \le 5\)\(t \le 10\)\(t \le 15\)\(t \le 20\)\(t \le 25\)\(t \le 30\)
Cumulative frequency2336\(a\)5153\(b\)

(d) Write down the values of \(a\) and \(b\).

This information is shown in the following cumulative frequency graph.

Cumulative Frequency Graph

(e) Use the graph to estimate the maximum time taken watching the octopus for the first 32 visitors (arranged in order of increasing viewing time).

(f) Use the graph to estimate the number of visitors who spent less than 13 minutes watching the octopus.

(g) Use the graph to estimate the number of visitors who take more than 17 minutes watching the octopus.

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