Sampling Distributions

When you take a sample out of the population it’s easy to measure the statistical data for that sample. Now, if a different sample was taken then the statistical data will most likely be different then the first one. This is because of sampling variation that can always happen when you take a sample. These values for all of the possible samples is called the Sample Distribution.

To show this we will take a coin and flip it. The theoretical probability of flipping a coin and getting heads is 50%. To check this, take a sample of 100 coin flips, 100 times. Now, instead of flipping a coin 100 times, recording the results of each flip, and then repeating this 100 times a computer program was used to simulate this. The sample distribution of this experiment is shown below.

Sample Distribution - Graph.png

The above table shows a relatively symmetrical distribution, and heads were flipped 51 times in twelve different samples. There appears to be an outlier with heads being flipped 31 times in a single sample. This graph does approximate what we expected from a theoretical perspective because 51% is close to 50%.

100 samples are far less than the total number of possible combinations from flipping a coin 100 times. The total number of possible combinations, which is approximately 1,267,650,000,000,000,000,000,000,000,000. However, in this case, this sample distribution is large enough to estimate the distribution of the entire population. Below is the sample distribution for 200 flips.

Sample Distribution - Graph 2.png

Comparing the two distributions are showing similar distributions. The only differences are that several of the lines are longer, and several of the empty spots are now showing results. Thus justifying our assumption that we have enough points of data to estimate the population distribution.