Question

Questions 2 and 3. Consider the following data set: {41, 48, 50, 50, 54, 57}.

Question 2. The standard deviation for the data set is ______?

A. 4

B. 3

C. 2

D. 5

E. 1

Question 3. How many of the numbers in the data set are within 0.75 SDs of the average?

A5

B. 2

C. 4

D. 3

E. 1

Answer 1

The data set given is {41, 48, 50, 50, 54, 57}.

Mean = x/n

=( 41 + 48 + 50 + 50 + 54 + 57) / 6

= 50

2) Standard deviation ={(1/n) (x - mean)2}

=(150/6)

= 5

3) We convert each value to its corresponding z score. The numbers which have z score less than 0.75 or greater than -0.75 are within 0.75 standard deviation of the mean.

z score = (x - mean)/standard deviation

After converting, the dataset is { -1.8 , -0.4 , 0 , 0 , 0.8 , 1.4}

Therefore, 48 , 50 and 50 are within 0.75 standard deviations of the mean.

Answer :3