4 The weights, \(w\) grams, of a random sample of 60 carrots of variety A are summarised in the table below.
| Weight | \(30 \leqslant w < 50\) | \(50 \leqslant w < 60\) | \(60 \leqslant w < 70\) | \(70 \leqslant w < 80\) | \(80 \leqslant w < 90\) |
| Frequency | 11 | 10 | 18 | 14 | 7 |
- Draw a histogram to illustrate these data.
- Calculate estimates of the mean and standard deviation of \(w\).
- Use your answers to part (ii) to investigate whether there are any outliers.
The weights, \(x\) grams, of a random sample of 50 carrots of variety B are summarised as follows.
$$n = 50 \quad \sum x = 3624.5 \quad \sum x ^ { 2 } = 265416$$
- Calculate the mean and standard deviation of \(x\).
- Compare the central tendency and variation of the weights of varieties A and B .