sketch distribution

Question

Brand new to stats and trying to solve this exercise that I found online. I don't want you to solve it for me, I just need a starting point to solve it myself. By "sketch" do they mean to show the 20 points on a graph? but what about sketching the mean...that seems to be more complicated......Thanks for any pointers

die tosses <- 5,4,4,2,5,6,3,2,2,1,5,5,5,4,6,3,2,5,6,4 Using a fair, six-sided die, toss it 20 times and record the number of dots that show up each time. Sketch the distribution of the data. Sketch the distribution of the sample average.

Construct a 90% confidence interval for the population mean. For this interval, use the standard deviation that you calculate in this sample

Answer 1

By "sketch the distribution" they probably mean a plot with 1,2,3,4,5,6 on the horizontal axis and on the vertical axis the number of times each result was observed; or the empirical probability of that result (which is just the number of times divided by the total number of rolls). This could be either six dots or six columns (if columns it will look like a histogram).

Sketching the distribution of the average is indeed much more complex and requires an understanding of what you would expect the average result to be if you repeated this 20-roll experiment many times. Try looking up "sampling distribution" and "central limit theorem". This will also help you answer the inference questions in the last paragraph.