ch 4 - Chapter 4 notes - Measures of dispersion represent...

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Chapter 4 notes - Measures of dispersion represent the spread or scatter of scores around a central point or the distinguish ability of scores. o Expressed in terms of distance along a distribution’s horizontal, X, axis. o Four measures of this are: 1) range 2) semi-interquartile range 3)standard deviation 4) index of dispersion - Measures of SKEWNESS and KURTOSIS represent the asymmetry and peakedness of data. FOUR MEASURES OF DISPERSION 1. Range--USED WITH MODE--DISTANCE MEASURE--QUANT. DATA - Simplest measure of dispersion - Distance between the largest/smallest scores. - Denoted by “R” and computed with formula: o R= X u (largest score) - X u (smallest score) INCLUSIVE RANGE o R= X j (midpoint largest score) - X j (midpoint smallest score) NONINCLUSIVE RANGE Often used in computer packages - the larger the range, the greater the spread or scatter of scores - not widely used!! o Value is determined by the two most extreme scores, so sampling stability is very poor.******* o Not mathematically tractable b/c can’t be manipulated arithmetically and algebraically. o Not meaningful for unordered qualitative data. o For QUANTITATIVE data: Range can be reported with the mode, giving a more complete picture of data. However, b/c mode is often used with unordered qualitative data, different measure of dispersion is needed. 2. Semi-Interquartile Range--W/ MEDIAN-DISTANCE MEASURE--QUANT. DATA - Based on two scores closer to the center of the distribution, so considerably more stable than R (range). - Denoted by “Q”, is ½ the distance between the first quartile point, Q 1, and the third quartile point, Q 3 . o Formula is: Q= (Q 3 -Q 1 )/ 2.
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o Computation similar to that of the median. (DIAGRAM BELOW-- pg. 92) o Semi-interquartile range, Q, is half the distance from Q 1 to Q 3 . - The larger the value of Q, the greater the distance between Q 1 and Q 3 , and the greater the spread or scatter of scores. - Often reported along with the median to give a more complete description of data. o IF SYMMETRICAL, median + or - semi-interquartile range (Mdn +/- Q) gives two points on X axis such that the interval between points contains 50% of scores, but ONLY IF ITS SYMMETRICAL!!! -
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This note was uploaded on 04/15/2008 for the course STATS 2402 taught by Professor Kirk during the Spring '08 term at Baylor.

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ch 4 - Chapter 4 notes - Measures of dispersion represent...

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