Median egg mass from a cumulative frequency curve, unknown class frequencies and grouped mean
Median egg mass from a cumulative frequency curve, unknown class frequencies and grouped mean
7 marks
The masses, \(m\) grams, of \(80\) eggs from a farm are summarised by the cumulative frequency curve below.
- Use the curve to estimate the median mass.[2]
The grouped frequency table below shows the same masses, where \(p,q\in\mathbb{N}\).
| Mass (\(m\) grams) | Number of eggs |
|---|---|
| \(50\leq m<54\) | \(6\) |
| \(54\leq m<58\) | \(14\) |
| \(58\leq m<62\) | \(p\) |
| \(62\leq m<66\) | \(21\) |
| \(66\leq m<70\) | \(q\) |
- Find \(p\) and \(q\).
- Using the table, estimate the mean mass of an egg, correct to four significant figures.[5]
Solution:
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Answer:(a) \(61.0\text{ g}\) (estimate from the curve) (b)(i) \(p=27,\ q=12\) (b)(ii) \(60.95\text{ g}\)
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