Question

data were collected from a typing class with 45 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 55 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 from the mean.

Step2: Analyze the new data - point

The class mean is 56 WPM and the new data - point is 55 WPM. The new data - point 55 is close to the mean 56.

Step3: Consider the effect on standard deviation

When a data - point close to the mean is added to the data set, it has a minimal effect on the spread of the data. Since the standard deviation measures spread, the standard deviation will be about the same, perhaps a little smaller as the new data - point makes the data more concentrated around the mean.

Answer:

The standard deviation would be about the same, perhaps a little smaller.