Chapter_3_1 - Numerical Measures of Center Chapter 2 (cont)...

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Chapter 2 (cont) Chapter 3: Association: Contingency, Correlation, and Regression Read Chapter 3 Quick Review of Last Lecture ± Graphical Display ² Qualitative variables: bar plots and pie charts ² Quantitative variables: histograms, stem and leaf plots, boxplots ± Numerical summary: ² Measures of center: mean, median ² Measures of spread: range, IQR = 75 th -25 th percentile ² Other measures of spread: variance, standard deviation ± Graphical and Numerical: Boxplot Numerical Measures of Center ± Mean ² Arithmetic mean, Sample mean ² Center of gravity ± Median ² the midpoint of the data, when data are ordered from lowest to highest ² 50th percentile, with half of the data above and half of the data below. ± Mode ² The local maximum of distribution ² The measurement that occurs most often ² Commonly used as a measure of popularity Measures of Dispersion, Spread, or Variability Range(data) = max(data) - min(data) Standard Deviation (formulas given soon) Variance (formulas given soon) Percentiles ² Arrange the data in order from smallest to largest ² The i-th percentile is the value that has at most i% of the measurements below it and at most (100 – i)% above ² Quartiles : 1 st , 2 nd or 3 rd are respectively the 25 th , 50 th , and 75 th percentiles. IQR (interquartile range)= 75 th percentile – 25 th percentile The Five-Number Summary ± The five-number summary of a dataset consists of the ² Minimum value ² First Quartile ² Median ² Third Quartile ² Maximum value Criteria for identifying an outlier ± An observation is a potential outlier if it falls more than 1.5 x IQR below the first quartile or more than 1.5 x IQR above the third quartile
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Boxplot ± A box goes from the Q1 to Q3 ± A line is drawn inside the box at the median ± A line goes from the lower end of the box to the smallest observation that is not a potential outlier and from the upper end of the box to the largest observation that is not a potential outlier. The potential outliers are shown separately Recall Logarithms x = log b y <---> b x = y . We say that
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Chapter_3_1 - Numerical Measures of Center Chapter 2 (cont)...

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