Mean substantially smaller than median symmetric mean

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Mean substantially smaller than median Symmetric: Mean roughly equal to median Skewed Right: Mean substantially greater than median Mean ≈ Median ≈ Mode Mean > Median > Mode Mean < Median < Mode
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Chapter 1: Exploring Data If a distribution is perfectly symmetric, the mean and the median are the same The mean is not resistant to outliers The mode, the data value that occurs the most often, is a common measure of center for categorical data Use the mean on symmetric data and the median on skewed data or data with outliers Spread : Standard deviation is the most common measure of spread. Range and IQR are also measures of spread. Distribution Shape Based on Boxplots: a. If the median is near the center of the box and each horizontal line is of approximately equal length, then the distribution is roughly symmetric b. If the median is to the left of the center of the box or the right line is substantially longer than the left line, then the distribution is skewed right c. If the median is to the right of the center of the box or the left line is substantially longer than the right line, then the distribution is skewed left Remember identifying a distribution from boxplots or histograms is subjective! Why Use a Boxplot? A boxplot provides an alternative to a histogram, a dotplot, and a stem-and-leaf plot. Among the advantages of a boxplot over a histogram are ease of construction and convenient handling of outliers. In addition, the construction of a boxplot does not involve subjective judgments, as does a histogram. That is, two individuals will construct the same boxplot for a given set of data - which is not necessarily true of a histogram, because the number of classes and the class endpoints must be chosen. On the other hand, the boxplot lacks the details the histogram provides. Dotplots and stemplots retain the identity of the individual observations; a boxplot does not. Many sets of data are more suitable for display as boxplots than as a stemplot. A boxplot as well as a stemplot are useful for making side-by-side comparisons. Five-number summary Min Q1 M Q3 Max smallest value largest value Boxplot First, Second and Third Quartiles (Second Quartile is the Median, M) [ ] * Outlier Lower Fence Upper Fence Smallest Data Value > Lower Fence Largest Data Value < Upper Fence (Min unless min is an outlier) (Max unless max is an outlier)
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Chapter 1: Exploring Data Example 1: Which of the following are resistant measures of central tendency: Mean, Range Median or Variance Mode? Standard Deviation IQR Example 2: Given the following set of data: 70, 56, 48, 48, 53, 52, 66, 48, 36, 49, 28, 35, 58, 62, 45, 60, 38, 73, 45, 51, 56, 51, 46, 39, 56, 32, 44, 60, 51, 44, 63, 50, 46, 69, 53, 70, 33, 54, 55, 52 What is the mean? What is the range? What is the median? What is the variance? What is the mode? What is the standard deviation?
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