## Practice Problems: Measures of Central Tendency - 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.

 Data Array 15 49 28 48 25 43 48 39 22 34 43 33 49 28 34 27 22 25 33 25 27 22 25 22 22 22 20 20 39 15

## Mean

 Mean = X / N = 452 / 15 = 30.13

## Median

 15 20 22 22 22 25 25 27 28 33 34 39 43 48 49

The median is 27. Half of the scores fall above this number and half fall below.

## Mode

Mode is equal to 22. It occurs 3 times; all other scores occur only 2 times or less

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

The mean number of minutes spent solving the problems on the computer was approximately 30 minutes. Half of the students spent more than 27 minutes solving the problems, and half spent less time solving the problems. More students spent 22 minutes solving the problems than any other amount of time.

## Is this data skewed?

The data indicate a slight positive skew. This is most likely due to the students who spent over 40 minutes working on the trigonometry problems. Note, that it is a very slight skew - only approximately a 3 minute difference between the mean and median.

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