The normal distribution -- also called the "Gaussian distribution" -- is a mathematical function often used in statistics to describe and model randomly distributed data that tend toward a mean -- or average -- value. Its graph is shaped like a bell that is centred about the mean value of the distribution and whose breadth varies with its standard deviation. Create graphs using online software tools to explore the normal distribution.

- Skill level:
- Moderately Easy

### Other People Are Reading

## Instructions

- 1
Navigate to Balasubramanian Narasimhan's page about the normal distribution at stat.stanford.edu. The tool that he provides updates the graph of a normal distribution as you change its mean and standard deviation, so you can quickly gain intuition of its basic properties.

- 2
Scroll down the page until you see the graph and its two sliders. Click and drag to adjust each slider, and watch how the graph changes.

- 3
Click the button to rescale the graph if your standard deviation is so small that the peak of the graph exceeds its bounds.

## Balasubramanian Narasimhan's Web Applet

- 1
Navigate to Stefan Waner's Function Evaluator and Grapher at people.hofstra.edu.

- 2
Type the expression for the normal distribution into the "y1=" field in the pink box. The expression must be formatted for the computer, so copy and paste the following, substituting the mean for "M" and the standard deviation for "S:"

1/sqrt(2

*pi*S)*e^(-.5*(x-M)^2/S) - 3
Specify the visible area of the graph using the text boxes in the blue box. If you are unsure of these settings, add the negative of the standard deviation to the mean, and use the result for the "Xmin" box. Add the standard deviation to the mean and use that value for the "Xmax" box. Enable both "Auto" checkboxes.

- 4
Click "Plot Graphs" in the blue box. Your graph appears in a new window.

## Stefan Waner's Function Grapher

- 1
Navigate to fooplot.com.

- 2
Input the expression for the normal distribution into one of the five input boxes along the right side of the page. Use the following expression, substituting the mean for "M" and the standard deviation for "S:"

1/sqrt(2

*pi*S)*e^(-.5*(x-M)^2/S) - 3
Click the "Plot it!" button beneath the text boxes. Your graph appears to the left.

- 4
Click the first "Custom" radio button in the "Plot options & window" area beneath the graph to specify the visible area of the graph. If you are unsure of what values to use, add the negative of the standard deviation to the mean and enter the result in the first text box. Add the standard deviation to the mean and use that value for the second box. Use "0" for the third box, and divide "1" by the square root of 6.28 times the standard deviation for the last box. Click "Reset" to adjust the viewing area.

- 5
Save your graph as a file in the "Take your graph with you" area at the bottom of the page. Select a format from the drop-down menu, and click "Save."