# Standard Deviation Applet - Instructions

Author(s):

### 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:

1. 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?
2. 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