3. The birth weights, in kg, of 1500 babies are summarised in the table below.
| Weight (kg) | Midpoint, xkg | Frequency, f |
| 0.0-1.0 | 0.50 | 1 |
| 1.0-2.0 | 1.50 | 6 |
| 2.0-2.5 | 2.25 | 60 |
| 2.5-3.0 | | 280 |
| 3.0-3.5 | 3.25 | 820 |
| 3.5-4.0 | 3.75 | 320 |
| 4.0-5.0 | 4.50 | 10 |
| 5.0-6.0 | | 3 |
$$\text { [You may use } \sum \mathrm { f } x = 4841 \text { and } \sum \mathrm { f } x ^ { 2 } = 15889.5 \text { ] }$$
- Write down the missing midpoints in the table above.
- Calculate an estimate of the mean birth weight.
- Calculate an estimate of the standard deviation of the birth weight.
- Use interpolation to estimate the median birth weight.
- Describe the skewness of the distribution. Give a reason for your answer.