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 student’s results were included in the data set, what effect would it have on the standard deviation?

Answer 1

Answer:

Standard deviation gets smaller

Step-by-step explanation:

No. of students = 45

The class had an average of 56 words per minute (WPM) with a standard deviation of 7 WPM.

$Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\56=\frac{Sum}{45}\\56 \times 45=Sum\\2520=Sum$

The teacher realized that the data from one student who typed 55 WPM was not entered.

So, new sum = 2520+55

New sum =2575

So, new mean =$\frac{2575}{45}$

New mean =57.22

Standard deviation is the measure of distance between observation and mean

So, if number gets closer to mean , Standard deviation gets smaller . if the numbers get bigger , Standard deviation gets bigger.

Since 55 is closer to 57.22

So, Standard deviation gets smaller