Question

As the sample size increases, what happens to the standard deviation of the sample distribution?

1) The standard deviation of the sample distribution increases
2) The standard deviation of the sample distribution decreases
3) The standard deviation of the sample distribution remains the same
4) The standard deviation of the sample distribution cannot be determined

Answer 1

As the sample size increases, the standard deviation of the sample distribution decreases.

Step-by-step explanation:

As the sample size increases, the standard deviation of the sample distribution decreases. This means that as more data points are included in the sample, the variability of the sample decreases, leading to a smaller standard deviation. It can be illustrated using an example:

In a small sample of 10 students' heights, the standard deviation may be 3 cm. However, if we increase the sample size to 100 students, the standard deviation may decrease to 1 cm. Therefore, the standard deviation of the sample distribution decreases as the sample size increases.