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STAT 1301

STAT 1301. Chapter 4 Measures of Center. 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 ”. Histogram Families by Size in 1988. Distribution of Families

lucretia-armando
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STAT 1301

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  1. 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”

  3. HistogramFamilies by Size in 1988 Distribution of Families by size in 1988 Family Size Source: Population Survey data tape

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

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

  6. 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

  7. WARNING ! • Averages are sensitive to extreme values.

  8. Salary Data Employee Hourly Wage 110-15-2436 5.00 109-16-4134 5.00 015-16-4134 5.00 101-45-1362 5.00 515-60-4142 5.00 612-45-36276.00 413-21-6561 6.00 218-35-4425 7.00 806-56-7132 8.00 Mr. Pearson 35.00

  9. Examples • 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 household income data • - AVG $57,208 • - Median $43,057

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

  11. “Center” of Histogram

  12. 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

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

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