What does it mean when a population is normally distributed?

Updated July 25, 2019. A normal distribution of data is one in which the majority of data points are relatively similar, meaning they occur within a small range of values with fewer outliers on the high and low ends of the data range.

How do you know if a sampling distribution is normally distributed?

On this site, we use the normal distribution when the population standard deviation is known and the sample size is large. We might use either distribution when standard deviation is unknown and the sample size is very large.

How do you test for normality?

The two well-known tests of normality, namely, the Kolmogorov–Smirnov test and the Shapiro–Wilk test are most widely used methods to test the normality of the data. Normality tests can be conducted in the statistical software “SPSS” (analyze → descriptive statistics → explore → plots → normality plots with tests).

Which two parameters define a normal distribution?

The graph of the normal distribution is characterized by two parameters: the mean, or average, which is the maximum of the graph and about which the graph is always symmetric; and the standard deviation, which determines the amount of dispersion away from the mean.

Is population distribution always normal?

In other words, regardless of whether the population distribution is normal, the sampling distribution of the sample mean will always be normal, which is profound! The central limit theorem (CLT) is a theorem that gives us a way to turn a non-normal distribution into a normal distribution.

What if the data is not normally distributed?

Many practitioners suggest that if your data are not normal, you should do a nonparametric version of the test, which does not assume normality. But more important, if the test you are running is not sensitive to normality, you may still run it even if the data are not normal.

What if the population is not normally distributed?

If the population has a normal distribution, then the sample means will have a normal distribution. If the population is not normally distributed, but the sample size is sufficiently large, then the sample means will have an approximately normal distribution.

When would the distribution of means be normally distributed?

The general rule is that if n is more than 30, then the sampling distribution of means will be approximately normal. However, if the population is already normal, then any sample size will produce a normal sampling distribution.

Is all data normally distributed?

Many everyday data sets typically follow a normal distribution: for example, the heights of adult humans, the scores on a test given to a large class, errors in measurements. The normal distribution is always symmetrical about the mean.