# Histogram

A If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency, the number of cases in each bin. In general, however, bins need not be of equal width; in that case, the erected rectangle has As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous. 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. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the 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. Another alternative is the average shifted histogram, which is fast to compute and gives a smooth curve estimate of the density without using kernels. The histogram is one of the seven basic tools of quality control. Histograms are often confused with bar charts. A histogram is used for continuous data, where the bins represent ranges of data, and the areas of the rectangles are meaningful, while a bar chart is a plot of categorical variables and the discontinuity should be indicated by having gaps between the rectangles, from which only the length is meaningful. Often this is neglected, which may lead to a bar chart being confused for a histogram. Histograms are often confused with bar charts. A histogram is used for continuous data, where the bins represent ranges of data, and the areas of the rectangles are meaningful, while a bar chart is a plot of categorical variables and the discontinuity should be indicated by having gaps between the rectangles, from which only the length is meaningful. Often this is neglected, which may lead to a bar chart being confused for a histogram. |

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