Descriptive Statistics
Measures of Variability
You should be able to . . .
• Define and compute the:
–Range
–Interquartile range
–Variance
•Parameter and statistic
–Standard deviation
•Parameter and statistic
• Define and explain
bias
• We have discussed
measures of central tendency
• Now we need measures to describe the degree to which
observations:
cluster together
or
differ or deviate
Measures of Variability
• Measures that indicate the degree of difference among
observations
Range
• A measure of variability that is the distance from the lowest
score to the highest score
• Range = (highest X  lowest X) + 1
Example Distribution
• What is the range?
• (230  80) + 1 = 151
Problems with the range
• Based on only two observations
• As number of observations increases, range increases
WHY?
• There is an increased probability of extreme values
Interquartile Range
1
2
3
4
5
6
7
8
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Interquartile Range
• Range for the middle 50% of the observations
–Chop off top 25% of observations
–Chop off bottom 25% of observation
Procedure for determining IQR
• 1.
Order observations from least to most
• 2.
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 Fall '07
 Pfordesher
 Standard Deviation, Variance, Statistical deviation and dispersion

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