#  RANDOM SAMPLING 

 



 **Random Sampling Creates a Representative Sample of the Target Population When Sample Size is Large Enough**  
By Elena Llaudet, co-author of [Data Analysis for Social Science: A Friendly and Practical Introduction (Princeton University Press, 2022)](https://press.princeton.edu/books/paperback/9780691199436/data-analysis-for-social-science)

 To simplify matters, imagine there were only five types of people in the world: orange, blue, pink, green, and purple. If we randomly select individuals from the population into a sample, the resulting sample will be representative of the population (that is, the sample will accurately reflect the characteristics of the population), if the sample size is large enough. Let's examine this further:

   ![Random Sampling with Sample Size = 20](/sites/g/files/omnuum9971/files/styles/hwp_1_1__720x720_scale/public/ellaudet/files/random_sampling_n_20.png?itok=qsXazq3w) 

 

When the sample size is very small, the sample will likely not be representative of the population because the sample size is simply too small to create a subset of individuals with a similar composition of different types as the population. As shown on the graph on the right, for example, if we select only 20 individuals from a target population of 1,000 individuals, the sample might end up with not a single blue individual eventhough the sample was created through random sampling. (Note about the graph: The histogram on the left shows the number of individuals from each type that are in the target population. The histogram on the right shows the number of individuals from each type that are in the sample. While N stands for the total number of individuals in the population, n stands for the total number of individuals in the sample.)   ![Random Sampling as Sample Size Increases](/sites/g/files/omnuum9971/files/styles/hwp_1_1__720x720_scale/public/ellaudet/files/random_sampling.gif?itok=tNibOR4i) 

 

Now, let's increase the sample size and observe how the composition of the sample starts to approximate the composition of the population as a result. (As we can see in the animated GIF on the right, as the sample size increases, the histogram of the sample starts to look a lot like the histogram of the population.) Once the sample size reaches 300, the composition of the sample is quite similar to the composition of the population. They are now both composed of roughly 20% orange individuals, 10% blue individuals, 20% pink individuals, 30% green individuals, and 20% purple individuals. (Looking for more animated GIFs and/or interactive graphs to help explain statistical concepts? Check my [website](/interactive-graphs-dss-readers).)