1. AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Descriptive Statistics: Chapter 3

2. 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

3. 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

4. Univariate Statistics of Dispersion 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 p 45

5. 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

6. 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):  MSD=143.54

7. 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): = 11.98 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

8. Standard deviation S or S X = 12.01 (3.6) n-1 is known as the degrees of freedom in calculating S X Univariate Statistics: Dispersion