STA 2023 Measure of Variation – 2.5
The range of a set of data is the difference between the highest value and the
lowest value.
The standard deviation of a set of sample values is a measure of variation of
values about the mean.
Weights. The weights of nine football players are recorded here.
206, 215, 305, 297, 265, 282, 301, 255, 261
1. Calculate the mean: x 
x
n
______________________
2. Subtract the mean from each individual value to get a list of deviations of
the form ( x  x ) .
3. Square each of the differences obtained from Step 2. This produces
numbers of the form ( x  x ) 2 .
4. Add all the squares obtained from Step 3. This is the value of
 ( x  x)
2
5. Divide the total from Step 4 by the number ( n – 1) ; that is, 1 less than
the total numbers of values present.
6. Find the square root of the result.
x
Totals:
Standard deviation =
x  xi
d
2
n 1
Calculating Standard
Deviation for Football
Players’ Weights
xx
( x  x) 2
.
The variance of a set of values is a measure of variation equal to the square
of the standard deviation.
Sample variance: Square of the standard deviation s.
Population variance: Square of the population standard deviation 
Finding Variance: In the preceding example, we found the standard deviation
of football players weights. Find the variance of that sample.
________________
Comparing Variation in Different Populations.
The coefficient of variation (or CV) for a set of sample or population data,
expressed as a percent, describes the standard deviation relative to the
mean, and is given by the following:
Sample
s
CV  100%
X
Population
CV 

100%

Heights and Weights of Men.
Pg. 764 , Data Set 1 in Appendix B. Fill in the table below using your calculator.
Mean ( X )
Height
Weight
Now, let’s calculate our coefficients of variation.
Heights:
Weights:
Standard Deviation(s)