Section 5.2: Which Tells the Truth – The Mean, The Median… or the Weighted Mean

Income US Census Bureau typically reports the median family income rather than the mean family income. If the distribution of data is symmetrical use either mean or median. If the distribution of data is skewed each gives a different result. Each has its own strength.

Median vs. Mean Data collection mistakes have little effect on median. The mean is related to the total in that it is the value you would use to predict what would happen in the long term.  Example: lottery

Mean vs. Median Since each has its own strength, report both. If these numbers are significantly different this will signal that the distribution of data is skewed or that severe outliers are present.  Example: Census Bureau

Measures of Center Only Tell Part of the Story Suppose that in this room there are 10 parents each of whom are 50 years old. Suppose that next door there are 5 twenty year olds and 5 eighty year olds. For each group, what’s the mean? the median?

Measures of Spread Measures of spread describe how far the data is from the center. When reporting numeric data always report both a measure of center and a measure of spread. Two common measures of spread are standard deviation and interquartile range. We’ll study both of these in Chapter 6.

Weighted Means Another type of measure of “average” which shows up in the news is a weighted mean. Shoppers should get some relief from credit card payments this year, as interest rates are starting to go down again… The weighted average annual percentage rate is percent this year for standard, gold, and platinum cards, compared with 18.11% percent in – Arizona Republic, November 28, 1998

Weighted Mean The weighted mean gives some measurements more weight and others less when you calculate a mean.  Example: Your course grade in MAT 170 is computed using a weighted mean.

Finding a weighted mean Each observation is first multiplied by its weight. Add up the products. Divide by the sum of the weights.