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

2. The Averages
Mean
Median
Mode
Trimmed Mean

3. 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

4. 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:

5. More on Median
Same median, should it represent the second group?

6. 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

7. 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