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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 | 154 |
| 2 | 121 |
| 3 | 160 |
| 4 | 135 |
| 5 | 140 |
| 6 | 134 |
| 7 | 129 |


A. 120
B. 136
C. [tex]$16 n$[/tex]
D. 168

Asked by jon444

Answer (1)

Calculate the mean of the sample means: 7 154 + 121 + 160 + 135 + 140 + 134 + 129 ​ .
The sum of the sample means is 973.
Divide the sum by the number of samples: 7 973 ​ = 139 .
The closest value to 139 among the choices is 136 ​ .

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.

Calculate the mean of sample means To find the best estimate, we calculate the mean of the given sample means:


7 154 + 121 + 160 + 135 + 140 + 134 + 129 ​

Sum the sample means Calculating the sum of the sample means:

154 + 121 + 160 + 135 + 140 + 134 + 129 = 973

Divide by the number of samples Now, divide the sum by the number of samples (7) to find the mean:

7 973 ​ = 139

Compare with the given choices The mean of the sample means is 139. Now we compare this value to the given choices: 120, 136, 16 n , and 168. The closest value to 139 is 136.

Examples
Estimating population parameters from sample data is a fundamental concept in statistics. For example, if you want to know the average income of people in a city, you can take several random samples of people and calculate the average income for each sample. The average of these sample means will give you a good estimate of the average income of the entire city's population. This is used in market research, political polling, and many other fields.

Answered by GinnyAnswer | 2025-07-04

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