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 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 problem 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