Reasoning with grouped frequencies
Reasoning with grouped frequencies
Secondary 2
8 marks
TGM Original Questions
Core stretch
The table shows the heights, \(h\) cm, of a group of students. The frequency \(p\) is a non-negative integer.
| Height (cm) | Frequency |
|---|---|
| \(120\le h<130\) | \(12\) |
| \(130\le h<140\) | \(18\) |
| \(140\le h<150\) | \(p\) |
| \(150\le h<160\) | \(15\) |
| \(160\le h<170\) | \(5\) |
The conditions in parts (a) and (c) are independent.
- Find the greatest possible value of \(p\) for which the middle observation, or both middle observations when the total frequency is even, lies or lie in the class \(130\le h<140\).[3]
- A student claims that a suitable choice of \(p\) can make \(150\le h<160\) the unique modal class. Explain why this is impossible.[2]
- Given instead that there are 60 students, find \(p\) and calculate an estimate of their mean height, correct to 1 decimal place.[3]
Solution:
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Answer:(a) \(p=9\). (b) Impossible: the fourth-class frequency 15 is less than the second-class frequency 18. (c) \(p=10\); estimated mean \(142.2\) cm.
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