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Histograms are sometimes confused with bar charts. The histogram is one of the seven basic tools of quality control. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot. The total area of a histogram used for probability density is always normalized to 1. Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. Examples of variable bin width are displayed on Census bureau data below.Īs the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous.

The vertical axis is then not the frequency but frequency density-the number of cases per unit of the variable on the horizontal axis. However, bins need not be of equal width in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin. A histogram may also be normalized to display "relative" frequencies showing the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. If the bins are of equal size, a bar is drawn over the bin with height proportional to the frequency-the number of cases in each bin. The bins (intervals) must be adjacent and are often (but not required to be) of equal size. The bins are usually specified as consecutive, non-overlapping intervals of a variable. To construct a histogram, the first step is to " bin" (or " bucket") the range of values-that is, divide the entire range of values into a series of intervals-and then count how many values fall into each interval.

The term was first introduced by Karl Pearson.

To roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values.Ī histogram is an approximate representation of the distribution of numerical data. For the histogram used in digital image processing, see Image histogram and Color histogram.