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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 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