4. A student collected data on the number of text messages, \(t\), sent by 30 students in her year group in the previous week. Her results are summarised as follows:
$$\Sigma t = 1039 , \quad \Sigma t ^ { 2 } = 65393 .$$
- Calculate unbiased estimates of the mean and variance of the number of text messages sent by these students per week.
(4 marks)
Another student collected similar data for 20 different students and calculated unbiased estimates of the mean and variance of 32.0 and 963.4 respectively. - Calculate unbiased estimates of the mean and variance for the combined sample of 50 students.
(6 marks)