Transcript Measures of Variability - Valdosta State University

Measures of
Variability
BUSA 2100, Section 3.2
Need for Measuring Variability
A sample of 5 deliveries is taken from
two suppliers.
 The delivery times in days are:
Adams Company {8, 10, 11, 15, 16};
Baker Company {1, 2, 7, 20, 30).
 Both sets of data have the same mean
of 12. But how do they differ?
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Measuring Variability, Page 2
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.
Range
Range=(biggest value)-(smallest value).
 Adams Company: range = 16 - 8 = 8
Baker Company: range = 30 - 1 = 29
Or just state as: 8 to 16, or 1 to 30.
 Easy to do, but not widely used.
 Uses only 2 items; influenced too much
by extreme values.

Interquartile Range
Interquartile Range (IQR) = Q3 - Q1;
the 3rd quartile minus the 1st quartile.
Or state as Q1 to Q3.
 Represents the middle 50% of the data.
 Overcomes the dependency on extreme
values.

Standard Deviation
Develop the formula for Adams Co. data
{8, 10, 11, 15, 16}. First, calculate the
deviations from the mean of 12.
 The deviations are:
 The “average deviation” would be the
sum divided by 5, but this is always zero
since the numerator is always 0.
 How can we keep the deviations from
“canceling out” and adding to zero?
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Standard Deviation, Page 2

.
Standard Deviation, Page 3
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Develop a chart showing X values,
X - Xbar values, and (X-Xbar)2 values.
Standard Deviation, Page 4
The formula for the standard deviation,
denoted by s is: (state on the board).
 For the Adams example, the answer =

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What does the standard deviation
mean? It has meaning, mostly in a
comparative sense.
Standard Deviation, Page 5

For the Baker Company example, the
standard deviation is 12.59 (as
compared to 3.39 for Adams Company).
Standard Deviation, Page 6
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The standard deviation is the most widely
used measure of dispersion. It uses all of the
data, and has many mathematical uses.
Together, the mean and the standard
deviation provide a good, brief summary for
data sets.