Assessing Normality: Normal Probability Plots


Statisticians often need tools to assess the normality of data. In other words, they need a way to answer the question: is the data normal or not?

One of the most basic ways to check is by seeing if the Empirical Rule applies. Where x̅ represents the sample mean and s represents the standard deviation, if and only if the data is normal, then:

68% of the data should be between x̅ +/- s

95% of the data should be between x̅ +/- 2s

99.7% of the data should be between x̅ +/- 3s 

Another method of assessing normality is creating a normal probability plot. 

If the data is normal, then the normal probability plot should be linear.


The Shapes of Normal Probability Plots

Symmetrical / Normal

(No Skew)

Skewed Right
Skewed Left


How to Create a Normal Probability Plot (TI-84)

Using a TI-84 calculator, follow these steps to create a normal probability plot:

1. Enter data into calculator by hitting 'STAT' and then 'Edit'

2. Hit '2nd' and then 'Y=' to access Stat Plot.

3. Enter Plot 1.

4. Turn Plot 1 'On' and then toggle below to 'Type.' Then click right until you get to the bottom right graph.

5. Hit 'ZOOM' and then scroll down to '9: Zoom Stat'