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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Descriptive Statistics: Chapter 3 Univariate Statistics of Central Tendency • There are three alternative statistics (i.e. formulas) to measure the central tendency of a variable: * The Mean * The Median * The Mode Univariate Statistics of Central Tendency • For example, if the 15 smallest deer weights are ignored; the mean increases from 61.77 Kg to 64.0 Kg while the median only goes from 64 Kg to 65Kg • The mode may be a useful statistic in the case of a discrete variable, but not for continuous variables because each observation value is likely to be unique Univariate Statistics of Dispersion p 45 • The range is a measure of dispersion given by the difference between the greatest and the smallest value of X in the n observations available Univariate Statistics: Dispersion The mean absolute deviation (MAD), MAD in deer weight = 9.00 Kg; max absolute deer weight deviation is 93 Kg - 61.77 Kg = 31.23 Kg min absolute deer weight deviation is 32 Kg – 61.77 Kg = -29.77 Kg Univariate Statistics: Dispersion • An alternative way to address the canceling out problem is by squaring the deviations from the mean to obtain the mean squared deviation (MSD): di 2 n MSD=143.54 X X 2 i n Univariate Statistics: Dispersion • Problem of squaring can be solved by taking the square root of the MSD to obtain the root mean squared deviation (RMSD): RMSD MSD X X 2 i = 11.98 n • When calculating the RMSD, the squaring of the deviations gives a greater importance to the deviations that are larger in absolute value, which may or may not be desirable Univariate Statistics: Dispersion • Standard deviation S or SX sX X X 2 i n 1 = 12.01 (3.6) • n-1 is known as the degrees of freedom in calculating SX