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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”