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Damian Dupuy

Measures of Dispersion  Range  Simplest measure of dispersion  Takes difference between smallest and largest value in the dataset, at the interval/ratio scale  But, influenced by outliers  Range = X max - min Quartiles  Can yield more information and lesson impact of outliers  Data are divided into quartiles (4 Groups)  Centiles (5 groups), Percentile (100 groups) Standard Deviation and Variance  Two of the most commonly used measures of dispersion  Comparing values of each measure to the Mean  Xi– X (x bar)  Two key properties of the mean/ value relationship o Sum of differences will always add up to Zero o Sum of the squared difference will be the minimum sum possible. Called “Least Squares” property o Least Squares property carries over into calculating ∑ ̅ o Variance: , second X has a bar ontop , x bar = sample mean ∑ ̅ o Standard Deviation √  Skewness o Measures the degree of symmetry in the frequency of distribution o Determine how evenly (or unevenly) the values are distributed either side of the mean ̅ o o You can only say if something is positively skewed or negatively skewed, there is no value of the difference  Coefficient of Variation o Allows for comparison of variability spatial samples – samples tied to a particular location o Tests which sample has the greatest variability o Standard Deviation or Variance are absolute measures, so they are influenced by the size of the values in the dataset – can’t compare among the samples because the scales will be different o Used for when you want to compare 2 locations. Ex. studying climatology and you are looking at rainfall in different areas, so you want to find which location has the greatest variability in rainfall?? Or looking at average household income, census data can be measured at the census tract level. And look at the variability in the census tracts, to see which one has the most variability o To allow a comparison of variation across two or more geographic samples,
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