1 The lengths, \(X \mathrm {~cm}\), of a sample of 100 insects of a certain type were summarised as follows.
$$n = 100 \quad \sum x = 36.8 \quad \sum x ^ { 2 } = 17.34$$
- Calculate unbiased estimates for the population mean and variance of \(X\).
- State a necessary condition for the estimates found in part (a) to be reliable.