Measures of Central Tendency 1

Study note – using audio slides 1 Advantages Revisiting them No attention lapses Nothing missed, everything available for comprehensive study guide come exam times More class time available for discussion/group work/explanation/SPSS Disadvantage Not real time lecture/no immediate interaction w/instructor Can result in wanting to ask questions, but not being able to Recommendation: Print slides before listening, make notes and write questions down as you go Email question/s if needed in order to make progress Listen to the slides early in the week so that there’s plenty of time to allow for communication with the instructor 2 3 4

Measure of Central Tendency What SINGLE summary statistic or parameter best describes the central location of an entire distribution? Mode: which value occurs most (what is fashionable) Median: the middle value in the data, once it’s ranked (the 50th percentile) Mean: mathematical balance point; arithmetic mean; mathematical mean 1 2 3 4 General note on this early stuff

Mode Most frequent occurrence What if data were 1 Most frequent occurrence What if data were 17, 19, 20, 20, 22, 23, 23, 28 Problem: set of numbers can be bimodal, or trimodal, depending on the scores Not a stable measure 2 3

Median Rank numbers, pick middle one What if data were 17, 19, 20, 23, 23, 28 Solution: add up two middle scores, divide by 2 (=21.5) Best measure in asymmetrical distribution (ie skewed), not sensitive to extreme scores 1 2

Mean Add up the numbers and divide by the sample size (number of numbers!) Try this one… 5,3,2,6,9 This is the best measure of the three – after all, it uses more information than any of the others 1 2 3

Characteristics of the Mean Balance point point around which deviations sum to zero Deviation is difference between two numbers For instance, if scores are 5,3,2,6,9 Mean is 5 Sum of deviations: 0+(-2)+(-3)+1+4 = 0 See? 1

Characteristics of the Mean Balance point Affected by extreme scores Scores 7, 11, 11, 14, 17 Mean = 12, Mode and Median = 11 Scores 7, 11, 11, 14, 170 Mean = 42.6, Mode & Median = 11 1

Characteristics of the Mean Balance point Affected by extreme scores Appropriate for use with interval or ratio scales of measurement 1

Characteristics of the Mean Balance point Affected by extreme scores Appropriate for use with interval or ratio scales of measurement More stable than Median or Mode when multiple samples drawn from the same population Basis for inferential stats 1

Guidelines to choose Measure of Central Tendency Mean is preferred because it is the basis of inferential statistics Median may be better for skewed data? Distribution of wealth in the US Mode to describe average of nominal data (Percentage - relative frequency) 1

Normal Distribution 1 Mode 2 Median 4 Mean Scores 3

Positively skewed distribution 1 2 Mode Median Mean Scores

Negatively skewed distribution 1 Mode Median 2 Mean Scores

End of file…variability next.