8 The heating quality of the coal in a sample of 50 sacks is measured in suitable units. The data are summarised below.
| Heating quality \(( x )\) | \(9.1 \leqslant x \leqslant 9.3\) | \(9.3 < x \leqslant 9.5\) | \(9.5 < x \leqslant 9.7\) | \(9.7 < x \leqslant 9.9\) | \(9.9 < x \leqslant 10.1\) |
| Frequency | 5 | 7 | 15 | 16 | 7 |
- Draw a cumulative frequency diagram to illustrate these data.
- Use the diagram to estimate the median and interquartile range of the data.
- Show that there are no outliers in the sample.
- Three of these 50 sacks are selected at random. Find the probability that
(A) in all three, the heating quality \(x\) is more than 9.5,
\(( B )\) in at least two, the heating quality \(x\) is more than 9.5.
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