Question

26. On an exam with a mean of M=39, you obtain a score of X = 35.

1. Would you prefer a standard deviation of s = 2 or s = 8? (Hint: Sketch each distribution and find the location of your score.)

2. If your score were X = 43, would you prefer s = 2 or s =  8? Explain your answer.

Answer 1

Ans:

when s=8

z=(35-39)/8=-0.5

when s=2

z=(35-39)/2=-2

when your score is below the mean,then you will prefer the larger standard deviation i.e. s=8,as you will be just 0.5 standard deviations below mean,and will get fair grade.

Now,when score is 43,it is above the mean.

when s=8

z=(43-39)/8=0.5

when s=2

z=(43-39)/2=2

when your score is above the mean,then you will prefer the smaller standard deviation i.e. s=2,as you will be 2 standard deviations above mean,and will get excellent grade.