 How to Calculate Descriptive Statistics Using Web Stat

1. Go to http://www.stat.sc.edu/webstat/
it will take a long time (up to a couple of minutes) to load if you are on a dial up connection. The last thing to appear will be the orange "Click here to fire it up!" button. 2. Click on the orange "Click here to fire it up!" button and a gray spreadsheet will appear. 3. Type the data in the "var 1" column like above.

4. After all the data has been entered, put your mouse on "Stat" then slide it down to "Summary Stats." The following dialog box will appear. 5. Click on "var1" in the gray portion and it will then also appear in the white portion, as shown below. 6. If you click the "Next->" button, the following dialog box will appear: 7. Remove the check marks in front of "Variance" and Std. Dev. by clicking on the box in front of them. 8. Press the "Calculate" button and the following results will appear: Results:

Summary Statistics:

 Variable n Mean Median Range Min Max var1 6 26.666666 25.5 11 23 34

.

 Variable Q1 Q3 Var1 24 28

9. Now comes the tricky part. Enter the value of the mean as an additional value in your variable column: 10. Again, put your mouse on "Stat" then slide it down to "Summary Stats." The following dialog box will appear. 11. Again, click on "var1" in the gray portion and it will then also appear in the white portion, as shown below. 12. Again, click the "Next->" button, the following dialog box will appear: 13. But this time, remove the check marks in front of everything but "Variance" and Std. Dev. by clicking on the box in front of the other statistics. 14. Again, press the "Calculate" button and the following results will appear: Results:

Summary Statistics:

 Variable n Mean Median Range Min Max var1 6 26.666666 25.5 11 23 34

.

 Variable Q1 Q3 Var1 24 28

.

Summary Statistics:

 Variable Variance Std. Dev. Var1 13.222222 3.636237428

Here is the logic behind what we did: WebStat calculates the variance based on (Sum of Squares / n-1). Adding the value of the mean to our data does not change the Sum of the Squared deviations as a the value of the mean minus the mean is zero and zero squared is zero. It does however increase the n by 1, so n + 1 - 1 = n. Therefore we trick WebStat into using (Sum of Squares / n) which is what we should use when we are calculating the variance and standard deviation on all the scores in the population.