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By observing the frequency distribution of a quantitative discrete or continuous variable, several shapes may be detected related also to the presence or absence of symmetry (Figures 1.3 and 1.4).

Figure 1.3 Shapes of distributions (symmetric and skewed distributions).

Figure 1.4 Other shapes of distributions.

If one side of the histogram (or bar chart for quantitative discrete variables) is close to being a mirror image of the other, then the data are fairly symmetric (a). Middle values are more frequent, while low and high values are less frequent. If data are not symmetric, they may be skewed to the right (b) or skewed to the left (c). In (b) low and middle values are more frequent than high values. In (c) high and middle values are more frequent than low values.

If histograms (or bar charts for quantitative discrete variables) show ever‐decreasing or ever‐increasing frequencies, the distribution is said to be J‐shaped (d). If frequencies are decreasing on the left side of the graph and increasing on the right side, the distribution is said to be U‐shaped (e). Sometimes there are values that do not fall near any others. These extremely high or low values are called outliers (f).