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Understanding Measures of Center: A Comprehensive Guide to Descriptive Statistics

This chapter focuses on the essential measures of center in statistics, which summarize data distributions effectively. It covers key concepts such as average (arithmetic mean), median, and mode, highlighting their significance and differences. The chapter illustrates how these measures apply to various data sets, including family sizes and salary data, and emphasizes the sensitivity of averages to outliers. Additionally, it introduces the Root Mean Square (RMS) as a valuable tool for analyzing data while ignoring signs, providing readers with a deeper understanding of descriptive statistics.

lucretia-armando
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Understanding Measures of Center: A Comprehensive Guide to Descriptive Statistics

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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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