What a grouped table can and cannot tell you
What a grouped table can and cannot tell you
IP 1
7 marks
The heights, \(h\text{ cm}\), of \(20\) students are recorded in a grouped frequency table.
| Height (cm) | \(150<h\le155\) | \(155<h\le160\) | \(160<h\le165\) | \(165<h\le170\) |
|---|---|---|---|---|
| Frequency | \(4\) | \(9\) | \(5\) | \(2\) |
- Explain why the exact mean height cannot be found from the table, and calculate an estimate of the mean.[3]
- Using the class boundaries, find the least and greatest values that the true mean could take.[2]
- State the class that contains the median, and explain why the median cannot be stated exactly.[2]
Solution:
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Answer:(a) heights are known only by class; estimate \(158.75\text{ cm}\) (b) \(156.25<\text{mean}\le161.25\) (c) \(155\lt h\le160\); the individual values are not recorded
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