Lengths of leaves in a “less than” table
Lengths of leaves in a “less than” table
Secondary 4
7 marks
The table shows the lengths, \(x\) cm, of \(50\) leaves.
| Length, \(x\) cm | \(4\le x<6\) | \(6\le x<8\) | \(8\le x<10\) | \(10\le x<12\) | \(12\le x<14\) |
|---|---|---|---|---|---|
| Frequency | \(3\) | \(9\) | \(17\) | \(13\) | \(8\) |
- Copy and complete the cumulative frequency table.[2]
| Length, \(x\) cm | \(x<6\) | \(x<8\) | \(x<10\) | \(x<12\) | \(x<14\) |
|---|---|---|---|---|---|
| Cumulative frequency |
- Find the number of leaves that are[3]
- less than \(10\) cm long,
- at least \(8\) cm long,
- at least \(6\) cm but less than \(12\) cm long.
- Explain why the number of leaves that are at most \(10\) cm long cannot be found from the table.[2]
Solution:
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Answer:(a) \(3,12,29,42,50\) (b)(i) \(29\) (ii) \(38\) (iii) \(39\) (c) Leaves exactly \(10\) cm long are counted in the class \(10\le x<12\) with longer leaves, so the table does not show how many are at most \(10\) cm.
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