1. Construction Engineering 221
Probability and statistics

2. 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)

3. 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

4. Measures of variance Measures of variance Range Absolute deviation
Standard deviation

5. 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

6. Measures of variance
Variance and Standard Deviation are derived similarly
Variance uses squares instead of absolute values to handle the negative number problem
Variance is a mean sum-of-squares of the individual differences from the mean (EQ 4-3, page 28)

7. Measures of variance
Standard deviation is simply the square root of the variance