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The average heights of four samples taken from a population of students are shown in the table. Which of these is most likely closest to the average height of the population?

\begin{tabular}{|c|c|}
\hline Sample size & \begin{tabular}{c}
Average height \\
(inches)
\end{tabular} \\
\hline 10 & 63 \\
\hline 20 & 54 \\
\hline 30 & 57 \\
\hline 40 & 59 \\
\hline
\end{tabular}

A. 54

B. 63

C. 59

D. 57



Answer :

GinnyAnswer
To determine which sample average height is most likely closest to the average height of the population, we need to consider the principle that larger sample sizes generally provide more reliable estimates of the population parameter because they tend to have lower sampling variability.

1. Given Data:

| Sample Size | Average Height (inches) |
|-------------|--------------------------|
| 10 | 63 |
| 20 | 54 |
| 30 | 57 |
| 40 | 59 |

2. Step-by-Step Analysis:
- We have four different sample sizes: 10, 20, 30, and 40.
- The corresponding average heights for these samples are 63 inches, 54 inches, 57 inches, and 59 inches, respectively.
- The fundamental idea is that the larger the sample size, the less variability and hence the more accurate the average will be as an estimate of the population's average height.

3. Identifying the Largest Sample Size:
- Out of the four given sample sizes (10, 20, 30, 40), the largest sample size is 40.

4. Corresponding Average Height:
- The average height corresponding to the sample size of 40 is 59 inches.

5. Conclusion:
- Since the sample with size 40 is the largest, its average height measurement of 59 inches is most likely the closest estimation to the average height of the entire student population.

Thus, the height most likely closest to the average height of the population is 59 inches.

Therefore, the correct answer is:
C. 59

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