Question

data were collected from a typing class with 10 students. the class had an average of 56 words per minute (wpm) with a standard deviation of 7 wpm. the teacher realized that the data from one student who typed 70 wpm was not entered. if this students results were included in the data set, what effect would it have on the standard deviation?
the standard deviation would be noticeably larger.
the standard deviation would be noticeably smaller.
the standard deviation would be about the same, perhaps a little larger.
the standard deviation would be about the same, perhaps a little smaller.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the spread of data. A value close to the mean has less impact on spread.

Step2: Calculate distance from mean

The mean of the original 10 - student data is 56 WPM. The new data point is 70 WPM. The difference from the mean is \(70 - 56=14\) WPM. Since the original standard deviation is 7 WPM, this new data point is \( \frac{14}{7} = 2\) standard - deviations away from the mean. Adding a data point that is relatively far from the mean will increase the spread of the data.

Answer:

The standard deviation would be noticeably larger.