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 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

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

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

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

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

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?

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

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

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

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)

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?