1. Chapter 4 Measures of Center
STAT 1301
Chapter 4
Measures of Center

2. It is often difficult to work with complete distributions.
So, we SUMMARIZE
Descriptive Measures of
Center
Spread
Today, we will concentrate on measures of “center”

4. Histogram Families by Size in 1988
Distribution of Families
by size in 1988
Familty Size
Family Size
Source: Population Survey data tape

5. Gas Mileage for Compact Cars%
per
unit
mpg
Miles per Gallon

6. Schematic Representations of Histogram
Symmetric
Long Right Tail
Long Left Tail
(skewed to the right)
(skewed to the left)

7. number of observations
Measures of Center
Average - arithmetic mean AVG =
Median - middle observation from ordered data
- middle value for an odd number of observations
- average of 2 middle values for even # of obs.
Mode - most frequently occurring observation
not necessarily unique
does not always exist
sum of observations
number of observations

9. WARNING !
Averages are sensitive to extreme values.

10. Salary Data Employee Hourly Wage 110-15-2436 5.00 109-16-4134 5.00
Mr. Pearson

11. Examples
Duke Univ. graduates of Dept. of Communications had an average starting salary of $418,000
- Grant Hill (NBA player)
Data on Household Income - which should be larger - AVG or median?
2002 – US household income data
- AVG $57,208
- Median $43,057

12. “Center” of Histogram Average - histogram balances
Median - divides histogram into equal parts based on area
Mode - modal class is the class interval with the highest bar

13. “Center” of Histogram

14. Root Mean Square (RMS) RMS size of a list: (S) square values in list
(M) sum squared values and divide by total # of values in list
(R) take square root
sum of squared values
RMS = # of values

15. RMS measures size of values in list ignoring signs
“sort of like average ignoring sign”