The mean of 10 readings of a variable was 8.7 with standard deviation 0.3. A further 5 readings were taken: 8.6, 8.5, 8.8, 8.7, and 8.9. Estimate the mean and standard deviation of the set of possible...

The mean of 10 readings of a variable was 8.7 with standard deviation 0.3. A further 5 readings were taken: 8.6, 8.5, 8.8, 8.7, and 8.9. Estimate the mean and standard deviation of the set of possible readings using all the data available.

Two samples are drawn from the same population as follows: sample 1 (0.4, 0.2, 0.2, 0.4, 0.3, and 0.3) and sample 2 (0.2, 0.2, 0.1, 0.4, 0.2, 0.3, and 0.1). Determine the best unbiased estimates of the population mean and variance.