Author(s):

Kady Schneiter (Utah State Univ.)

### Investigate the standard deviation of a distribution

- Click on boxes in the grid to create a distribution of numbers.
- The number of filled cells in any column indicates the number of times the corresponding column value occurs in the distribution.
- Clicking on the topmost filled box in any column clears the column.
- Clicking on any unfilled box in the column fills the column to the selected cell.

- The mean of the distribution is indicated by a green triangle.
- The size of the standard deviation is shown by the blue bar.
- Use the spinners at the top to change the number of rows or columns.
- The mean and standard deviation indicators can be toggled on or off using the check boxes at the top.
- Use the "show values" checkbox to show the numeric values of the mean and standard deviation.

**Note:** The standard deviation computed is the *population* standard deviation.

### Activity

Use the applet to explore the size of the standard deviation as you change the distribution on the grid.

Set the number of rows to 6 and the number of columns to 10. Investigate the following:

- What is the smallest value of the standard deviation that you can find for a distribution involving at least two distinct numbers (that is, at least two different columns should be shaded)?
- Can you create more that one distribution that yields this minimum standard deviation?
- Can you get this standard deviation from a distribution that involves at least three distinct numbers?
- Under what circumstances is the standard deviation small?

- What is the largest value of the standard deviation that you can find for a distribution involving at least two distinct numbers?
- Can you create more that one distribution that yields this maximum standard deviation?
- Under what circumstances is the standard deviation large?

Kady Schneiter (Utah State Univ.), "Standard Deviation Applet - Instructions," *Convergence* (February 2010), DOI:10.4169/loci003212