Question

Let's say I am interested in creating a sampling distribution with 25 students per sample to calculate the average number of credits PCC students are taking this term. In your own words, describe how we would create a histogram to represent a sampling distribution 25 observations per sample. For full credit, make sure your solution distinguishes your answer from a population distribution, and a sampling distribution of proportions.

Answer 1

In order to create a histogram to represent a sampling distribution 25 observations per sample, first we generate the sample of size 25 from population distribution and use this sample to calculate the sample mean, say
11
. Next we repeat this process say M tiimes and thus obtain the sample means $\bar{x}=(\bar{x}_1, \cdots, \bar{x}_M)$ . We use these sample means to create the histogram. To do that we need bins and then corresponding frequency count. Bins,denoted by k can be choosen as

$k=\frac{\max{(\bar{x})}-\min{(\bar{x})}}{h}$

The histogram is used to visualise the distribution. Here we can see from histogram that what the distribution of the sample means looks like. It can be symmetric, skewed, unimodal, bimodal etc.