Question

What is the difference between data that is normally distributed versus data that is not? What can you say about small sample sizes? How many standard deviations from the mean is considered unusual and why?

Typed responses only please :)

Answer 1

For a normally distributed data, the graph is symmetric about the mean, in such cases mean , Median and mode are equal . It has a bell shaped curve structure. Where as the data is not normal may have many modes , and the graph may be skewed, non symmetric and so on.

According to the central limit theorem, if the sample size is sufficiently large enough then the sampling distribution of the sample mean is approximately normal regardless of the distribution of the sample.

*Data beyond two standard deviations away from the mean is considered "unusual" data.As a general rule, z-scores lower than -1.96 or higher than 1.96 ( 2 tailed)

arec considered unusual and interesting. That is, they are statistically significant outliers.