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Descriptive Statistics
Involves computing summary
measures and constructing
graphs, tables and charts to
illustrate those measures
Measures of Location
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Arithmetic Mean or Average;
Median;
Mode; and
Weighted Average
Measures of Variability or
Spread
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Range;
Variance;
Standard Deviation, and
Coefficient of Variation
Measures of Location
Measures of location describe data by
providing a central tendency (location)
value for the data
Arithmetic Mean or
Average
Population:
x = (Xi) / N
where:
x = population
mean;
Xi = the ith value in
the data set;
 = summation
symbol; and
N = population size
Sample:
X = (Xi) / n
where:
X = sample mean;
Xi = the ith value in the
data set;
 = summation
symbol; and
n = sample size
Median
The median is the middle observation in
data that have been arranged in
ascending or descending numerical
sequence
Median = (n + 1) / 2 ranked
observation
where n = number of observations
Mode
The mode is the value in a set of data
that appears most frequently
Weighted Average
A weighted average is an arithmetic
mean for which each value (X) is
weighted (W) according to some welldefined criterion
Xw =
(XW) / W
Measures of Variability or
Spread
Measures of variability or spread
describe data by indicating the extent
of the differences between the values of
a data set
Range
The range of the data set is the
difference between the largest and
smallest values in the set
Range = Largest Value - Smallest Value
Variance
The variance provides a numerical
measure of how the data tend to vary
around the arithmetic mean
x2
=  ( Xi -
s2 =

x )2 / N
for populations
( Xi - X )2 / (n - 1) for samples
Standard Deviation
The standard deviation may be thought
of as a measure of distance from the
mean
STD = SQRT of Variance
Population:
=
SQRT OF
Sample:
2
S = SQRT of S2
Coefficient of Variation
The coefficient of variation is a measure
of relative variation
Population:
Sample:
V = ( / x ) * 100
V = ( S / X ) * 100
where:
V = Coefficient of Variation