# What is the sample size?

The sample size refers to the significant proportion that is drawn from the population that meets the objectives of the research. It is used a lot to perform Market studies and commercial investigations.

Thus, the size of the sample will benefit the researcher in not spending so much to know the population data and will be calculated based on the established budget and time. Thus, the sample size depends on:

• The size of the population. It is a collection of objects that gathers characteristics that interest us. It can be: target or theoretical population, which has several characteristics; or accessible population, on which the researchers apply their conclusions.
• Margin of error or confidence interval. It is the statistical margin of error in the results of a survey.
• Confidence level. They are random intervals that allow you to limit a high probability value. It is usually represented in% and represents that the result of a certain action will meet the expectations of that percentage.
• Standard deviation. It indicates the dispersion of the data, so if it is large, the more dispersed it is.

## Sample's size calculation

There are two ways to calculate the sample size:

### We do not know the size of the population

If we do not know the size of our population, the formula to know the size of the sample is as follows:

n = [(Z^2 * p * q) / d^2]

Being:

Z: the confidence level;

P: probability of success;

Q: probability of failure;

D: accuracy or maximum permissible error that we will admit, in%

### We know the size of the population

Otherwise, in which we know the size of the population, we can apply the following formula:

n = (N*Z^2*P*Q) / [d^2 * (N-1) + Z^2*P*Q]

Being:

N: population size

Z: the confidence level;

P: probability of success;

Q: probability of failure;

D: accuracy or maximum permissible error that we will admit, in%

Categories S