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Central Tendency & Variability Dec. 7

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Central Tendency Summarizing the characteristics of data Provide common reference point for comparing two groups of data Mode, median, mean

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Mode The value in a distribution of values within a data set that occurs most frequently Ages of clients (n=15) –28,31,38,39,42,42,42,42,43,47,51,54,55 Years of prior work experience –0,0,0,0,1,2,2,3,4,5,5,5,7,7,7,7,8,9,11,14

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Of the three measures of central tendency, the mode is the most unrestricted Has the fewest requirement for its use Used with nominal level of measurement

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Data can be formed into an array Median divides an array of values into two equal halves Number of treatment session –2,2,2,3,3,4,5,6,7,8,9,10,11,11,41 (n=15) –1,1,1,1,2,2,3,4,5,6,6,7,8,8,9,10 (n=16) Be aware of outlier Used with ordinal level of data Median

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Mean Typical value of that variable The sum of all the values in a distribution divided by the total number of values (average) Scores of final test –65,65,70,70,75,75,75,80,85,85,85,85,90,90,95

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Variability How widely the data vary from the typical value Indicator of the degree of variation among values or value categories Dispersion –21,22,24,24,26,29,30,31,32,33,36,38,38,40,41 –27,28,28,29,29,30,30,31,32,32,33,33,34,34,35

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Range Distance that encompasses all values within a data set R= maximum value – minimum value + 1 What are the ranges for section 1 and 2 of the course?

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Mean Deviation The average amount that the values of a variable differ from the mean Describes only the amount of variation, not their absolute values Sum of deviation values Mean deviation = ---------------------------- number of cases

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Exercise Find the mean deviation for following data set –1,2,3,4,5

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Variance Subtracting the mean of the distribution from each value (the mean deviation) Squaring each difference Dividing the sum of squared differences by the number of cases

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Standard Deviation The square root of the variance Requires interval or ratio level of data Years of employment –5,5,6,6,7,7 (agency A) –1,2,4,8,10,11 (agency B)

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Exercise 89,56,45,78,98,45,55,77,88,99,98,97,54,34,94 77,88,87,67,98,87,55,77,45,44,88,99,69,67,98 Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Which section did better overall on the exam?

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