Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 60Figure 2.14 Histogram of waitingwith density estimate2.3.2 Modes, symmetry, and skewUsing the histogram and density estimate of a univariate data set, we can broadly classifythe distribution according to the number of peaks, the symmetry, and the size of the tails.These attributes are essential to know when we want to make statistical inferences aboutthe data.ModesA mode of a distribution is a peak, or a local maximum, in its density (found using thedensity estimate). A data set can be characterized by its number of modes. A unimodaldistribution has a single mode—it occurs at “the mode.” The mode is sometimes used torepresent the center of a distribution. Distributions with two modes are termed bimodaldistributions; those with two or more modes are multimodal distributions.For example, the waiting data set shown in Figure 2.14 is bimodal. The data setgalaxies (MASS) shown in Figure 2.15 is an example of a multimodal data set. In thesame figure, we see that the OBP data set could be considered unimodal if the BarryBonds outlier is removed from the data.SymmetryA univariate data set has a symmetric distribution if it spreads out in a similar way tothe left and right of some central point. That is, the histogram or density estimate shouldhave two sides that are nearly mirror images of one another. The OBP data set (Figure2.15) is an example of a symmetric data set if once again the Barry Bonds outlier isremoved. The waiting data set in Figure 2.14 is not symmetric.Another type of a symmetric data set is the “well-shaped” distribution. These