STAT 1301 Chapter 4 Measures of Center

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

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

Gas Mileage for Compact Cars Miles per Gallon % per unit mpg 10 5

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

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

WARNING! l Averages l Averages are sensitive to extreme values.

Salary Data Employee Hourly Wage Mr. Pearson Employee Hourly Wage Mr. Pearson 35.00

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

“Center” of Histogram l Averagebalances l Average - histogram balances l Median equal l Median - divides histogram into 2 equal parts based on area l Mode highest l Mode - modal class is the class interval with the highest bar

“Center” of Histogram

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

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