Question

 

Suppose that a researcher observed the aggressive behavior of 100 college students. She ends up with a distribution of 100 scores that have a mean of 20 and a standard deviation of 8. Specify what will happened to the mean and standard deviation in each of the following cases.

 

a. What is the new mean if 8 is added to each score? (1 points)

 

 

b. What is the standard deviation if 8 is added to each score? (1 points)

 

 

c. What is the standard deviation if each core is multiplied by 4? (1 points)

Answer 1

Solution:
Given in the question
Number of student = 100
Mean. =20
Standard deviation = 8
Solution(a)
We need to find the new mean if 8 is added to each score
If every number is increase by 8 than total sum of 100 numbers will increase by (8*100) = 800
so average will increase by = 800/100 = 8
So new average will be = old mean + New mean = 20+ 8 = 28
Solution(b)
What is the standard deviation if 8 is added to each score
Standard deviation can be calculated as
Standard deviation = sqrt((Xi-mean)^2/(n-1))
As we are increase 8 to every number than mean also increase than (Xi-mean)^2 will remain same so standard deviation will also same.
So New Standard deviation if 8 is added to each score = 8
Solution(c)

If each core is multiplied by 4 than standard deviation will also multiplied by 4 so new standard deviation = 8*4 = 32