Measures of Central Tendency Measures of central tendency tell us something about the “typical-ness” of a set of data. Tell us what the typical score is in a distribution of scores. Three measures of central tendency: Mode Median Mean

Measures of central tendency: mode The mode is the score that occurs most frequently in a distribution. Sometimes more than one score occurs at frequencies distinctively higher than other scores, in which case there is(are) more than one mode: Bi-modal distributions. Multi-modal distributions. Only appropriate measure of central tendency for nominal data.

Measures of central tendency: median The median is the middle score in an ordered distribution of scores. It is the score that divides a distribution in half. It is also the score at the 50th percentile rank. The median is the most appropriate measure of central tendency for ordinal data.

Measures of central tendency: median In the distribution given to the right, find the median. What is the percentile rank (PR) of a score of 13? What is the score cor-responding to a percentile rank of 15? Score Freq Cum. F %c 6 2 2 3.8 8 5 7 13.5 9 0 7 13.5 10 8 15 28.8 11 11 26 50.0 12 9 35 67.3 13 6 41 78.8 14 4 45 86.6 15 5 50 96.2 16 2 52 100.0

Measures of central tendency: mean The mean is the arithmetic average value of a distribution (of scores). I Xi represents the score for individual i (in a distribution of size n) on the variable X, then Xi / n gives the mean of the distribution of X.

Measures of central tendency: mean For the distribution of GPAs given to the right. What is the mean GPA? Ans.: 2.71 A distribution of GPAs Case GPA 1 2.56 2 3.04 3 2.88 4 3.25 5 1.80