Find the range, sample standard deviation, and sample variance
for the following four data sets.
Please use the statistics mode on your calculator
for these four data sets.
Fabricated data based on annual earnings of select
individuals related to producing this homework assignment:
$36,000, $360,000, $3,600,000, $36,000,000, and $360,000,000
(teacher, notebook assembler, Netscape® programmer,
Windows® programmer, Bill Gates).
Data set with mixed precision: 1, 1.1, 2.7, 3.14, 1.618.
Data set with an even number of elements: 1, 2, 3, 4, 5, 6, 7, 8.
Data set with lots of data
(inauguration ages of U.S. presidents):
57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48,
65, 52, 56, 46, 54, 49, 51, 47, 55, 55, 54, 42, 51, 56,
55, 51, 54, 51, 60, 62,
43, 55, 56, 61, 52, 69, 64, 46, 54.
Sort the presidential inauguration age data on your calculator.
Count how many data elements are within one standard deviation of
the mean (i.e. between 54.8-6.2=48.6 and 54.8+6.2=61.0).
Convert this to a percentage.
Repeat the previous question with two standard deviations instead of one.
Consider again the sample data 1, 1, 2, 4, 7.
Explicitly calculate the standard deviation using the first
formula given in the lecture.
Explicitly calculate the standard deviation using the shortcut
formula given in the lecture.
Bonus: Derive the shortcut formula for the standard deviation
from the first formula given.
One of the rounding rules we omitted was that if you are going to
take a square root you can only retain half as many significant figures
as was in the radicand. This has significance related to standard
deviations. Find the square root of 5 and
round this result to three significant figure.
Now square this result and also result±0.01.
Compare the three answers in terms of how a 2 parts per thousand (ppk)
change (0.01/5) had an x ppk affect on the result.