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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 & 61 \\
\hline 20 & 52 \\
\hline 30 & 55 \\
\hline 40 & 57 \\
\hline
\end{tabular}

A. 61

B. 55

C. 57

D. 52

Sagot :

GinnyAnswer
To determine which average height is most likely closest to the average height of the population, we should consider the principle that larger sample sizes tend to provide estimates that are more representative of the entire population. This is because larger sample sizes generally reduce the impact of random variation or anomalies that might be present in smaller samples.

Let's analyze the given data:

1. Sample size: 10, Average height: 61 inches
2. Sample size: 20, Average height: 52 inches
3. Sample size: 30, Average height: 55 inches
4. Sample size: 40, Average height: 57 inches

Among these, the sample with the largest size is 40. Therefore, the average height corresponding to the largest sample size is most likely to be the closest representation of the population's true average height.

The average height for the sample of size 40 is 57 inches.

As a result, the correct option is:

C. 57
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