Transcript or the Weighted Mean

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.
http://www.census.gov/hhes/www/income/statemedfaminc.html


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 18.08 percent this year for standard, gold, and
platinum cards, compared with 18.11% percent in 1997.
– 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.
