3. An agriculturalist is studying the yields, \(y \mathrm {~kg}\), from tomato plants. The data from a random sample of 70 tomato plants are summarised below.
| Yield ( \(y \mathrm {~kg}\) ) | Frequency (f) | Yield midpoint ( \(x \mathrm {~kg}\) ) |
| \(0 \leqslant y < 5\) | 16 | 2.5 |
| \(5 \leqslant y < 10\) | 24 | 7.5 |
| \(10 \leqslant y < 15\) | 14 | 12.5 |
| \(15 \leqslant y < 25\) | 12 | 20 |
| \(25 \leqslant y < 35\) | 4 | 30 |
$$\text { (You may use } \sum \mathrm { f } x = 755 \text { and } \sum \mathrm { f } x ^ { 2 } = 12037.5 \text { ) }$$
A histogram has been drawn to represent these data.
The bar representing the yield \(5 \leqslant y < 10\) has a width of 1.5 cm and a height of 8 cm .
- Calculate the width and the height of the bar representing the yield \(15 \leqslant y < 25\)
- Use linear interpolation to estimate the median yield of the tomato plants.
- Estimate the mean and the standard deviation of the yields of the tomato plants.
- Describe, giving a reason, the skewness of the data.
- Estimate the number of tomato plants in the sample that have a yield of more than 1 standard deviation above the mean.