STAT 1301STAT 1301

Chapter 4Chapter 4

Measures of CenterMeasures of Center

It is often difficult to work It is often difficult to work with complete distributions.with complete distributions.

So, we SUMMARIZESUMMARIZE

Descriptive Measures ofDescriptive Measures of CenterCenter SpreadSpread

Today, Today, we will concentrate on measures of we will concentrate on measures of ““centercenter””

Histogram Families by Size in 1988Distribution of Families

by size in 1988

Family Size

Source: Population Survey data tape

Gas Mileage for Compact Cars

Miles per Gallon

%perunitmpg

10

5

Schematic Representations of Histogram

Symmetric

Long Right Tail (skewed to the left)

Long Left Tail(skewed to the left)

Measures of Center 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

WARNINGWARNING !!

Averages Averages are sensitive to extreme values.

Salary DataSalary Data

Employee Hourly Wage110-15-2436 5.00109-16-4134 5.00015-16-4134 5.00101-45-1362 5.00515-60-4142 5.00612-45-3627 6.00413-21-6561 6.00218-35-4425 7.00806-56-7132 8.00Mr. Pearson 35.00

Employee Hourly Wage110-15-2436 5.00109-16-4134 5.00015-16-4134 5.00101-45-1362 5.00515-60-4142 5.00612-45-3627 6.00413-21-6561 6.00218-35-4425 7.00806-56-7132 8.00Mr. Pearson 35.00

ExamplesExamples

1995 - 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 US household income data - AVG $57,208

- Median $43,057

““Center” of HistogramCenter” of Histogram

AverageAverage - histogram balancesbalances

MedianMedian - divides histogram into 2 equalequal parts based on area

ModeMode - modal class is the class interval with the highest highest bar

““Center” of HistogramCenter” of Histogram

RMSRMS 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 RMSRMS = # of values

Root Mean Square (RMS)

RMSRMS

measures size of values in list ignoring signs

“sort of like average ignoring sign”