Sheri surveyed eighty students and then generated three random samples of twenty-five student responses. The means of the samples are shown below.
| Sample | Mean |
| -------- | ---- |
| Sample 1 | 12 |
| Sample 2 | 16 |
| Sample 3 | 13 |
Looking at the table of sample means, which value is the best estimate of the mean of the population?
A. 10
B. 12
C. 14
D. 16
Answer (1)
Average the sample means: ( 12 + 16 + 13 ) /3 = 13.67 .
Round to the nearest option provided.
The best estimate of the population mean is 14 .
Explanation
Understand the problem We are given the means of three random samples taken from a population of eighty students. Our goal is to estimate the mean of the entire population using these sample means. The best estimate for the population mean is the average of the sample means.
Plan the solution To find the best estimate of the population mean, we need to calculate the average of the three sample means. The sample means are 12, 16, and 13.
Calculate the average We calculate the average of the sample means by adding them together and dividing by the number of samples, which is 3. So, the calculation is:
( 12 + 16 + 13 ) /3 = 41/3 = 13.666666666666666
The average of the sample means is approximately 13.67.
Determine the best estimate Looking at the given options (10, 12, 14, 16), the closest value to our calculated average (13.67) is 14. Therefore, the best estimate of the mean of the population is 14.
Examples
Estimating the average income of residents in a city by surveying a few neighborhoods and averaging their average incomes. This gives a reasonable estimate without surveying every single resident.
