Consider the following table of the ages of our first six presidents. Ages of th
ID: 3024141 • Letter: C
Question
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
Explanation / Answer
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)