Question

Describe how the variability of the distribution changes as the sample size increases. As the sample size increases, the variability decreases. It cannot be determined. As the sample size increases, the variability stays the same. As the sample size increases, the variability increases.

Answer 1

Answer:

As the sample size increases, the variability decreases.

Step-by-step explanation:

Variability is the measure of actual entries from mean.  The less the deviations the less would be the variance.

For a sample  of size n, we have by central limit theorem the mean of sample follows a normal distribution for random samples of large size.

X bar will have std deviation as $\frac{s}{\sqrt{n} }$

where s is the square root of variance of sample

Thus we find the variability denoted by std deviation is inversely proportion of square root of sample size.

Hence as sample size increases, std error decreases.

As the sample size increases, the variability decreases.