Consider the following table of the ages of our first six pr

Consider the following table of the ages of our first six presidents. Ages of the First 6 Presidents at Inauguration: Washington 57, J. Adams 61, Jefferson 57, Madison 57, Monroe 58, J.Q. Adams 57
a. Find the mean of the data set. Round to 2 decimal places.
b. Find the standard deviation (showing all the work). Do not use the statistical abilities of your calculator. You should use 2 decimal places for all non-squared number and 2 decimal places for your final answer.
c. How many of the presidents’ ages fall within one standard deviation of the mean?

***I need to have an explanation for EACH step taken, and correct ROUNDING of the anwers

Solution

Washington 57
J. Adams 61
Jefferson 57
Madison 57
Monroe 58
J.Q. Adams 57
a.
Mean of the data = ( 57 + 61 + 57 + 57 + 58 + 57)/6 = 57.83

b.
Step 1:Add them up:
57 + 61 + 57 + 57 + 58 + 57 = 347

Step 2: Square your answer:
347 × 347 = 120409
…and divide by the number of items. We have 6 items in our example so:
120409 / 6 = 20068.167
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
57^2+61^2+57^2+57^2+58^2+57 ^2= 20081

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
20081 - 20068.167 = 12.833
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
6 – 1 = 5

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
12.833/ 5 = 2.5666
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

2.5666 = 1.6021

c.

About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.
(u ± 1s.d)