Investigate the standard deviation of a distribution.
Note: The standard deviation computed is the population standard deviation.
- 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.
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?