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In Mathematics / College | 2025-07-04

Looking at this table of sample means, which value is the best estimate of the mean of the population?

| Sample | Sample Mean |
|---|---|
| 1 | 16.8 |
| 2 | 12.3 |
| 3 | 19.0 |
| 4 | 17.5 |
| 5 | 18.2 |
| 6 | 17.5 |

A. 11.0
B. 12.3
C. 17.3
D. 20.9

Asked by jon444

Answer (2)

Calculate the mean of the sample means: 6 16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 ​
Sum the sample means: 16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 = 101.3
Divide the sum by the number of samples: 6 101.3 ​ = 16.883333333333333
Choose the closest value from the options: The best estimate of the mean of the population is 17.3 ​ .

Explanation

Understand the problem We are given a table of sample means and asked to estimate the population mean. The best estimate for the population mean is the average of the sample means.

Identify the sample means To find the best estimate, we need to calculate the mean of the given sample means. The sample means are 16.8, 12.3, 19.0, 17.5, 18.2, and 17.5.

Calculate the mean of sample means We calculate the mean of the sample means by adding them up and dividing by the number of samples, which is 6. So, the calculation is: 6 16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 ​

Sum the sample means The sum of the sample means is: 16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 = 101.3

Divide by the number of samples Now, we divide the sum by the number of samples: 6 101.3 ​ = 16.883333333333333

Compare with the options The mean of the sample means is approximately 16.88. Now we compare this value to the given options: 11.0, 12.3, 17.3, and 20.9. The closest value to 16.88 is 17.3.

State the final answer Therefore, the best estimate of the mean of the population is 17.3.


Examples
Estimating population parameters from sample data is a fundamental concept in statistics. For example, if you want to know the average height of all students in a university, you can take several random samples of students, measure their heights, and then calculate the average of the sample means. This average provides a good estimate of the average height of all students in the university. This method is widely used in various fields such as market research, quality control, and scientific studies to make inferences about a larger population based on smaller samples.

Answered by GinnyAnswer | 2025-07-04

To estimate the mean of the population from the sample means, we calculate their average, which is approximately 16.88. The closest value from the options provided is 17.3. Thus, the answer is C. 17.3.
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Answered by Anonymous | 2025-07-12

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