Estimating quartiles and a time limit from a cumulative frequency table
Estimating quartiles and a time limit from a cumulative frequency table
IP 2
8 marks
The finishing times of \(200\) runners in a race are summarised in the cumulative frequency table.
| Time \(t\) (minutes) | \(t\le20\) | \(t\le25\) | \(t\le30\) | \(t\le35\) | \(t\le40\) |
|---|---|---|---|---|---|
| Cumulative frequency | \(0\) | \(30\) | \(110\) | \(170\) | \(200\) |
Assume that within each class the times are spread evenly.
- Estimate the median time.[2]
- Estimate the interquartile range.[2]
- The organisers want \(90\%\) of runners to finish within the time limit. Estimate the time limit they should set.[2]
- Explain why the estimate in (c) might be unreliable.[2]
Solution:
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Answer:(a) \(29.4\) min (b) \(7.08\) min (c) About \(36.7\) min (d) Even spread within a class is an assumption; race-day runners may differ
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