Question

Use the following data obtained from ages of the last six U. S. Presidents at the time of their inauguration to answer the following questions:

Ages of Last 6 Presidents at Inauguration
Ronald Reagan 69
George Bush 64
Bill Clinton 46
George W. Bush 54
Barack Obama 47
Donald Trump 70
a. Find the mean of the data set. (Round to one decimal place.)
b. Find the standard deviation of the data set. (Do not round until the final answer. Round final answer to 1 decimal place.)
c. What percentage of presidents' ages fall within one standard deviation of the mean

Answer 1

a) The mean of the data set is 58.3.

b) The standard deviation of the data-set is of 10.8.

c) 50% of presidents' ages fall within one standard deviation of the mean

Explanation:

Question a:

Sum of all values divided by the number of values.

`M = (69 + 64 + 46 + 54 + 47 + 70)/(6) = 58.3`

The mean of the data set is 58.3.

Question b:

Square root of the sum of the difference squared between each value and the mean, divided by the number of values subtracted by 1. So

`S = \sqrt{((69-58.3)^2 + (64-58.3)^2 + (46-58.3)^2 + (54-58.3)^2 + (47-58.3)^2 + (70-58.3)^2)/(5)} = 10.8`

The standard deviation of the data-set is of 10.8.

Question c:

Between 58.3 - 10.8 = 47.5 and 58.3 + 10.8 = 69.1.

3 out of 6(Reagan, Bush and W. Bush), so:

3*100%/6 = 50%

50% of presidents' ages fall within one standard deviation of the mean