Question

How can I tell if my data is normally distributed? Do the mean, median and mode have to be identical for it to be a normal distribution?

Answer 1

The data should be mound-shaped and symmetrical.

Explanation:

A set of data points is approximately normal if it is mound-shaped and symmetrical.
More closely, 68% of the data will fall within one standard deviation of the mean.
95% of the data will fall within 2 standard deviations of the mean.
99.7% of the data will fall within 3 standard deviations of the mean.

The mean, median, and mode might be equal and a distribution may still not be normal. For example:

0 0 0 0 0 0 0, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10.

The mean, median, and mode are each 5, but the data are not mound-shaped and symmetrical. This distribution is not normal.