The following data are from a simple random sample.
5 8 10 7 10 14
a. What is the point estimate of the population mean?
b. What is the point estimate of the population standard deviation?
a. The point estimate of the population mean is the average of the sample data. To find this, we add up all the numbers and divide by the total number of data points:
5 + 8 + 10 + 7 + 10 + 14 = 54
Since there are 6 data points, the point estimate of the population mean is:
54 / 6 = 9
b. The point estimate of the population standard deviation is the sample standard deviation. To find this, we first subtract the mean from each data point, square the result, sum up all the squared differences, divide by n-1 (where n is the number of data points), and then take the square root of the result:
(5-9)^2 + (8-9)^2 + (10-9)^2 + (7-9)^2 + (10-9)^2 + (14-9)^2 = 66
Dividing by n-1, which is 6-1 = 5, we get:
66 / 5 = 13.2
Finally, taking the square root, we get:
√13.2 ≈ 3.63
So, the point estimate of the population standard deviation is approximately 3.63.