Histogram

Study notes

• Purpose stated as (Chambers): graphically summarize the distribution of a univariate data set.
• The histogram shows the center (location), spread (scale), skewness, presence of outliers and presence of multiple modes, giving indications of a suitable distributional model.
• A probability plot or a goodness-of-fit test can be used to verify the distributional model.
• The cumulative histogram is a variant in which the vertical axis gives the count for a bin plus all bins for smaller values of the response variable.
• Relative histogram and relative cumulative histogram are variants in which counts are replaced by normalized counts.
• Normalization method 1: count in a class divided by the total number of observations, so relative counts sum to one (or 100 if a percentage scale is used).
• Normalization method 2: count in the class divided by the number of observations times the class width, so the area under the histogram equals one.
• With the area normalization, relative frequencies greater than 1 are permissible; use it when overlaying a probability density or cumulative distribution function.
• Histograms can answer: what kind of population distribution the data come from, where data are located, how spread out they are, whether they are symmetric or skewed, and whether outliers exist.
• Related techniques listed: box plot and probability plot; frequency plot, stem and leaf plot and density trace are similar in purpose but not discussed in the Handbook.
• Demonstrated in the heat flow meter data case study; the sample plot is a histogram of the Michelson speed of light data set.
• Available in most general purpose statistical software programs and in most charting, spreadsheet and business graphics programs.