# Using Simple Random Sample to Study Larger Populations

Simple random sampling is a method used to cull a smaller sample size from a larger population and use it to research and make generalizations about the larger group. It is one of several methods statisticians and researchers use to extract a sample from a larger population; other methods include stratified random sampling and probability sampling. The advantages of a simple random sample include its ease of use and its accurate representation of the larger population.

## How a Simple Random Sample Is Generated

Researchers generate a simple random sample by obtaining an exhaustive list of a larger population and then selecting, at random, a certain number of individuals to comprise the sample. With a simple random sample, every member of the larger population has an equal chance of being selected.

Researchers have two ways to generate a simple random sample. One is a manual lottery method. Each member of the larger population group is assigned a number. Next, numbers are drawn at random to comprise the sample group. if a simple random sample were to be taken of 100 students in a high school with a population of 1,000, then every student should have a one in ten chance of being selected.

The manual lottery method works well for smaller populations, but it isn't feasible for larger ones. In these situations, researchers prefer computer-generated selection. It works via the same principle, but a sophisticated computer system, rather than a human being, assigns numbers and selects them at random.

## Room for Error

With a simple random sample, there has to be room for error represented by a plus and minus variance. For example, if in that same high school, a survey were to be taken to determine how many students are left-handed, random sampling can determine that eight out of the 100 sampled are left-handed. The conclusion would be that 8% of the student population of the high school are left-handed, when in fact the global average would be closer to 10%.

The same is true regardless of the subject matter. A survey on the percentage of the student population that has green eyes or is physically incapacitated would result in a high mathematical probability based on a simple random survey, but always with a plus or minus variance. The only way to have a 100% accuracy rate would be to survey all 1,000 students which, while possible, would be impractical.