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Construction Engineering 221
Probability and statistics
Measures of variance
• Three things you need to know about a
sample or a population in order to
understand it
– What is the nature of its distribution?
– Where is the center (location measure)
– How far is the data distributed from the center
(variance measures)
Measures of variance
• If X samples have similar means, they
may not be similar samples, so variance
must be incorporated into the analysis
• If for any samples, the mean and
standard deviation are approximately
equal, we can then say there are no
statistical differences in the samples
Measures of variance
• Measures of variance
– Range
– Absolute deviation
– Variance
– Standard deviation
Measures of variance
• Range is simplest- largest minus smallest
• Range loses much information and does
not have much statistical power
• Mean absolute deviation- measures the
average (mean) deviation of each
observation (EQ 4-1, page 26)
• MAD is simple to calculate, simple to
understand, but lacks statistical power for
sample comparisons
Measures of variance
• Variance and Standard Deviation are
derived similarly
• Variance uses squares instead of absolute
values to handle the negative number
• Variance is a mean sum-of-squares of the
individual differences from the mean (EQ
4-3, page 28)
Measures of variance
• Standard deviation is simply the square
root of the variance