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
492401
482304
431849
391521
341156
331089
28784
27729
25625
25625
22484
22484
22484
20400
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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