MEASURES OF CENTRAL TENDENCY One number hoping to represent an entire pile of data… the average

The Averages Mean Median Mode Trimmed Mean

The Arithmetic Mean Usually meant when one says “average” =sum/# of items… Ex/n “x bar” for sample “mu” for population Based on numeric values An example: Fred’s test scores; 93, 67, 38, 74, 95 Another example: Our class siblings Can be affected easily by outliers… pulled in that direction

The Median Another number used to represent an entire collection of numbers The middle value when the numbers have been ordered small to large Think middle of the freeway, the median that your mother tells you not to hit with the new rolls Position is emphasized, not numeric values…so it is resistant to outliers (an advantage over the mean) An example: Our class siblings Another example: 13 15 17 19 21

More on Median 13 15 17 18 21 21 13 13 17 18 321 4321 Same median, should it represent the second group?

The Mode Another “average” It is simply the most often occurring value… the most frequently seen Overlooked, but often more appropriate. For instance the average size hat, or suit, or shoe. Can be bimodal, and may be no mode Outliers do not affect this average

Trimmed Means A mean that resists extremes… it has character A mean that eliminates the pull of extremely low or high values in the data set An example: find the 10% trimmed mean for class siblings with Sean McD