Statistics Definitions > What is a Normal Probability Plot?

## What is a Normal Probability Plot?

When you have a set of data that you think might have a normal distribution (i.e. a bell curve), a graph of your data can help you decide whether or not your data is normal. Making a histogram of your data can help you decide whether or not a set of data is normal, but there is a more specialized type of plot you can create, called a **normal probability plot**. A normal probability plot graphs z-scores (normal scores) against your data set.

A straight, diagonal line means that you have normally distributed data. If the line is skewed to the left or right, it means that you *do not* have normally distributed data.

## What is a Normal Probability Plot used for?

It can be easy to see with a **histogram** how data fits the norm, or skews from the norm.

With a normal probability plot, it can be easier to see individual data items that don’t quite fit a normal distribution. In the image below, the upper right data item is clearly out of line with the rest of the data, meaning that it doesn’t fit with a normal distribution.

## How to Draw a Normal Probability Plot

### By Hand

**Note**: you may want to watch the Excel video below as it explains many of these steps in more detail:

- Arrange your x-values in ascending order.
- Calculate f
_{i}= (i-0.375)/(n+0.25), where i is the position of the data value in the

ordered list and n is the number of observations. - Find the z-score for each f
_{i} - Plot your x-values on the horizontal axis and the corresponding z-score

on the vertical axis.

Normal probability plots aren’t normally drawn by hand, because the normal scores used for the plot can’t be looked up in a table. That’s why technology like Minitab or SPSS is usually used to create these types of graphs. You can also use Excel to create a simple normal probability plot:

**Note:** It’s best to make a histogram of your data to make sure it’s normally distributed before you make a normal probability plot. That’s because it’s easier to see a bell curve on a histogram that it is to gauge whether or not your data is normally distributed on a straight line (or almost straight line).

Reference: University of Northern Colorado.

Hi, Bill. I’m really iemepssrd with the Common Core overall, and the Prob and Stats component in particular. And I like very much what the progressions documents do. I haven’t read the progressions in a great deal of depth, but I did read looking for a couple particular things in 7th grade as they came up in a workshop I was doing. Standard 7.SP.3 Informally assess the degree of visual overlap of two numericaldata distributions with similar variabilities, measuring the differencebetween the centers by expressing it as a multiple of a measure ofvariability. will be difficult for teachers to understand. And once it’s explained I think they’ll have trouble understanding the point. I suggest that this should be expressed directly in the progression doc. Specifically an example showing the same different in means with different spreads. Maybe the larger spread example could be two samples from the same population, for example. Then keep the means the same but show a small spread, and clarify how using the measure of variability as your gauge is a way of assessing overlap. The idea is somewhat discussed, but I don’t think this important point is made clear.

what is the value fi

See step 2 under How to Draw a Normal Probability Plot

By Hand. It has the equation to calculate it. Did you watch the Excel video?