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Central Tendency & Variability

Central Tendency & Variability. Dec. 7. Central Tendency. Summarizing the characteristics of data Provide common reference point for comparing two groups of data Mode, median, mean. Mode . The value in a distribution of values within a data set that occurs most frequently

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Central Tendency & Variability

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  1. Central Tendency & Variability Dec. 7

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

  3. 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

  4. 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

  5. Median • 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

  6. 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

  7. 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

  8. 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?

  9. 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

  10. Exercise • Find the mean deviation for following data set • 1,2,3,4,5

  11. 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

  12. 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)

  13. 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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