## Practice Problems: Measures of Variability - Answer

A high school teacher at a small private school assigns trigonometry practice problems to be worked via the net. Students must use a password to access the problems and the time of log-in and log-off are automatically recorded for the teacher. At the end of the week, the teacher examines the amount of time each student spent working the assigned problems. The data is provided below in minutes.

 X X2 49 2401 48 2304 43 1849 39 1521 34 1156 33 1089 28 784 27 729 25 625 25 625 22 484 22 484 22 484 20 400 15 225 452 15160

## Standard Deviation

 S = 15 (15160) - 4522 15 (15-1)

S = 10.48718

## Variance

The variance is 109.98095. The standard deviation is 10.48718. The variance is the square of the standard deviation. 10.48718 squared is equal to 109.98095.

S2 = 109.98095

## Range

The range is 34. The high score is 49; the low score is 15. 49 - 15 = 34.

Range = 34

## What does this information tell you about the variability of students' length of time on the computer solving trigonometry problems?

It depends on how you look at the question. If you look at the mean of approximately 30 minutes. Then having a standard deviation of approximately 10.5 minutes seems rather large. But if you put it in the broader context, a standard deviation of approximately 10.5 minutes of study time is not all the big.

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