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What is a Histogram?

Welcome to the Investors Trading Academy talking glossary of financial terms and events. Our word of the day is “Histogram”. A histogram is a graphical representation of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" the range of values—that is, divide the entire range of values into a series of small intervals—and then count how many values fall into each interval. A rectangle is drawn with height proportional to the count and width equal to the bin size, so that rectangles abut each other. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins or intervals must be adjacent, and usually equal size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous. Histograms give a rough sense of the density of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis is all 1, then a histogram is identical to a relative frequency plot. A histogram can be thought of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. By Barry Norman, Investors Trading Academy