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 student's results were included in the data set, what effect would it have on the standard
deviation?
O The standard deviation would be noticeably larger.
O The standard deviation would be noticeably smaller.
O The standard deviation would be about the same, perhaps a little larger.
O The standard deviation would be about the same, perhaps a little smaller.

Question

09-09-2022
Mathematics

contestada

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 student's results were included in the data set, what effect would it have on the standard
deviation?
O The standard deviation would be noticeably larger.
O The standard deviation would be noticeably smaller.
O The standard deviation would be about the same, perhaps a little larger.
O The standard deviation would be about the same, perhaps a little smaller.

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joaobezerra joaobezerra · Answer 1 · 2022-09-15T21:35:31+02:00

The correct option regarding the standard deviation of the data-set adding observation 55 is:

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

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.

The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

For this problem, we have that an observation of 55 has a difference squared of 1 with the mean, which is less than the variance of 7² = 49, hence the mean of the differences squared would suffer a small decay(small due to the sample size), and would the standard deviation, hence the correct option is given by:

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

More can be learned about the standard deviation of a data-set at https://brainly.com/question/12180602

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