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Measures of Variability (Dispersion) Measures of Variability Range – Range = (High Score - Low Score+1) – Summary of Range Least stable-based on only two scores in distribution Can’t compare across distributions of different sample sizes. With small samples, about as good as any measure. – .e.g... Used in quality control Range is used with mode. Measures of Variability Range Semi-Interquartile Range – Defines a range on either side of the Mdn. which contains the middle 50% of the scores Measures of Variability Semi-Interquartile Range Q Q Q 3 1 2 Of course to actually do this, we have to know how to calculate Q3 & Q1 Measures of Variability Semi-Interquartile Range – Q2 and the Mdn. are the same thing. – Q1 Point on scale above which 75% of the scores fall and below which 25% fall. – Q3 Point on scale above which 25% of the scores fall and below which 75% fall. Now lets get down to how we do these calculations . Measures of Variability Semi-Interquartile Range – Q2 is the median, and we calculate the other quartiles just like the median, but we use n/4 instead of n/2. Measures of Variability Semi-Interquartile Range 115.75 90 Q 12.875 2 •The middle 50% of of scores fall between: 91.005 - 116.755 Measures of Variability Semi-Interquartile Range – Summary Mdn. is used with Q Mdn. Q defines range including middle 50% of scores. Q is more stable since it isn’t influenced by extreme scores like the range. Measures of Variability Range Semi-Interquartile Range Average Deviation – – – – Computed by averaging the deviation of each score from the mean. Problem is, sum is always zero so average is not possible. This is solved by using absolute values The problem with this is that the result can only be used for description and is not useful for any subsequent calculations. – Is used with the Mean - 1AD marks a range including 58% of the scores. Measures of Variability Range Semi-Interquartile Range Average Deviation N AD x 1 N k AD x (X X) fx 1 N mp Measures of Variability Range Semi-Interquartile Range Average Deviation Standard Deviation s Measures of Variability Standard Deviation s Raw (Ungrouped) data N s x 1 N N x 2 OR s = X X 2 1 N 1 Measures of Variability Standard Deviation s Raw (Ungrouped) data Next we will see how to compute the standard deviation. You will see that there are lots of ways to calculate this important statistic - they all yield an important descriptive statistic - THE STANDARD DEVIATION Press Armadillo to Return to Class Page….