Question

Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia, on June 20, 2013. Assume that the population is approximately normal. 4.912 4.636 4.555 4.231 4.476 4.658 4.791 3.395 4.228 4.873 4.311 4.541 4.912 4.636 4.555 4.231 4.476 4.658 4.791 3.395 4.228 4.873 4.311 4.541 4.912 4.636 4.555 4.231 4.476 4.658 4.791 3.395 4.228 4.873 4.311 4.541 (a) Find the sample standard deviation s . Round the answer to at least four decimal places. The sample standard deviation s is

Answer 1

To calculate the sample standard deviation of the given sample the mean has to be calculated first as:

Mean = (4.912 + 4.636 + 4.555 + 4.231 + 4.476 + 4.658 + 4.791 + 3.395 + 4.228 + 4.873 + 4.311 + 4.541 + 4.912 + 4.636 + 4.555 + 4.231 + 4.476 + 4.658 + 4.791 + 3.395 + 4.228 + 4.873 + 4.311 + 4.541 + 4.912 + 4.636 + 4.555 + 4.231 + 4.476 + 4.658 + 4.791 + 3.395 + 4.228 + 4.873 + 4.311 + 4.541)/36
= 160.821/36
= Mean = 4.4673

And the sample standard deviation is calculated as:

Standard Deviation s = √(1/36 - 1) x ((4.912 - 4.4673)² + ...................+ ( 4.541 - 4.4673)²)
= √(1/35) x ((0.4447)² + .......................................+ (0.073700000000001)²)
= √(0.0286) x ((0.19775809) + .............................+ (0.0054316900000001))

= √(0.0286) x (5.49754884)

= √(0.157229896824)

= 0.3963