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 income 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).
range = 359,964,000 or rather 360,000,000
standard deviation = 157,249,587.4 or rather 160,000,000
sample variance = 2.5 × 1016
Data set with an even number of elements: 1, 2, 3, 4, 5, 6, 7, 8.
range = 7 or 7.0
standard deviation = 2.4
sample variance = 6.0 (not 5.8 from 2.42
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 54.9-6.3=48.5 and 54.9+6.3=61.2).
Convert this to a percentage.
30 data elements are in [49,61] or 71.4%
Consider again the sample data 1, 1, 2, 4, 7.
Explicitly calculate the standard deviation using the first
formula given in the lecture.
{(1-3)2 + (1-3)2 + (2-3)2
+ (4-3)2 + (7-3)2}/4 = {4 + 4 + 1 + 1 + 16}/4 = 6.5
is the variance
Now, take the square root. The standard deviation is 2.6.