{Exercise 7.11}
The following data are from a simple random sample.
3, 8, 11, 6, 11, 15
What is the point estimate of the population mean?
9
What is the point estimate of the population standard deviation (to 1 decimal)?
To find the point estimate of the population mean, you take the average of the sample values. In this case, the sample values are:
3, 8, 11, 6, 11, 15
To find the point estimate of the population mean, add up all the values and divide by the number of values:
(3 + 8 + 11 + 6 + 11 + 15) / 6 = 54 / 6 = 9
Therefore, the point estimate of the population mean is 9.
Now, to find the point estimate of the population standard deviation, you use the formula for the sample standard deviation. However, since we only have a sample, not the entire population, we can only estimate the standard deviation based on this sample.
The formula for the sample standard deviation is:
s = √[ Σ(x - x̄)² / (n - 1) ]
Where:
s = sample standard deviation
x = each value in the sample
x̄ = sample mean (which we already found to be 9)
Σ = summation
n = number of values in the sample
Using the given sample values, we can calculate the sample standard deviation:
(3 - 9)² + (8 - 9)² + (11 - 9)² + (6 - 9)² + (11 - 9)² + (15 - 9)² / (6 - 1)
= 6² + (-1)² + 2² + (-3)² + 2² + 6² / 5
= 36 + 1 + 4 + 9 + 4 + 36 / 5
= 90 / 5
= 18
Therefore, the point estimate of the population standard deviation is 18 (to 1 decimal place).