Question

Suppose the following data show the introductory interest rates on a sample of 5 credit cards: 5.3, 2.3, 2.9, 4.3, 3.8. Calculate the standard deviation of the sample. Note: the numbers may be different from the last problem. (please express your answer using 2 decimal places)

Answer 1

Answer: 1.18

Explanation:

Let m be mean

Mean= sum/ n

Mean= (5.3+2.3+2.9+4.3+3.8 ) / 5

m= 18.6 / 5

M= 3.72

Mean= 3.72

Standard deviation sample formula is:

S.D= sqrt((|x-m|^2) / n-1)

So let start with |x-m|^2

For 1st: |5.3-3.72|^2=2.4964

For 2nd: |2.3-3.72|^2=2.0164

For 3rd: |2.9-3.72|^2=0.6724

For 4th: |4.3-3.72|^2=0.3364

For 5th: |3.8-3.72|^2=0.0064

Summation of |x-m|^2 = 5.528

Standard deviation sample formula is:

S.D = sqrt((summation of |x-m|^2) / n-1)

S.D=sqrt(5.528 / 4)

S.D=sqrt(1.382)

S.D=1.176

S.D=1.18 to 2 decimal place