When it comes to scientific studies, sample size is a crucial consideration for quality research. Sample size, sometimes represented as *n*, is the number of individual pieces of data used to calculate a set of statistics. Larger sample sizes allow researchers to better determine the average values of their data and avoid errors from testing a small number of possibly atypical samples.

#### TL;DR (Too Long; Didn't Read)

Sample size is an important consideration for research. Larger sample sizes provide more accurate mean values, identify outliers that could skew the data in a smaller sample and provide a smaller margin of error.

## Sample Size

Sample size is the number of pieces of information tested in a survey or an experiment. For instance, if you test 100 samples of seawater for oil residue, your sample size is 100. If you survey 20,000 people for signs of anxiety, your sample size is 20,000. Larger samples sizes have the obvious advantage of providing more data for researchers to work with; but large sample-size experiments require larger financial and time commitments.

## Mean Value and Outliers

Larger samples sizes aid in determining the average value of a quality among tested samples -- this average is the *mean*. The larger the sample size, the more precise the mean. For instance, if you find that, among 40 people, the mean height is 5 feet, 4 inches, but among 100 people, the mean height is 5 feet, 3 inches, the second measurement is a better estimation of the average height of an individual, since you're testing substantially more subjects. Determining the mean also allows researchers to more easily pinpoint *outliers*. An outlier is a piece of data that differs strongly from the mean value and can represent a point of interest for research. So based on the mean height, someone with a height of 6 feet, 8 inches, would be an outlying data point.

## The Danger of Small Samples

The possibility of outliers is part of what makes large sample size important. For instance, say you survey 4 people about their political affiliation, and one belongs to the Independent party. Since this is one individual in a sample size of 4, your statistic will show that 25 percent of the population belongs to the Independent party, likely an inaccurate extrapolation. Increasing your sample size will avoid misleading statistics if an outlier is present in your sample.

## Margin of Error

Sample size is directly related to a statistic's *margin of error*, or how accurate a statistic can be calculated to be. For a yes-or-no question, such as whether an individual owns a car, you can determine the margin of error for a statistic by dividing 1 by the square root of the sample size and and multiplying by 100. The total is a percentage. For instance, a sample size of 100 will have a 10 percent margin of error. When measuring numerical qualities with a mean value, such as height or weight, multiply this total by two times the *standard deviation* of the data, which measures how spread out the data values are from the mean. In both cases, the larger the sample size, the smaller the margin of error.