Business, Legal & Accounting Glossary
A histogram is an accurate representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. It differs from a bar graph, in the sense that a bar graph relates two variables, but a histogram relates only one. 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 intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins must be adjacent and are often of equal size.
The histogram is a well-known graphing tool. It is used to summarise discrete or continuous data on an interval scale. It is frequently used to depict the major elements of data distribution in an easy-to-understand format. A histogram categorises or groups the range of possible values in a data set. A rectangle is built for each group, with a base length equal to the range of values in that group and an area equivalent to the number of observations in that group. This implies that the rectangles will be drawn with varying heights. A histogram resembles a vertical bar graph in appearance, but when the variables are continuous, there are no gaps between the bars. However, when the variables are discrete, spaces should be left between the bars.
The following are the distinctions between a vertical bar graph and a histogram:
A histogram will often have bars of equal width, however, this is not always the case when class intervals differ in size. It is critical to select the appropriate width of the bars for a histogram. As shown in the above example, the histogram is essentially a series of vertical bars. The variable under consideration is measured on an arithmetic scale along the horizontal x-axis. The bars are all the same width and correspond to the same class intervals, whereas the height of each bar shows the frequency of the class it represents.
The histogram is used for variables with numerical values that are measured on an interval scale. It is commonly utilised when working with huge data sets (greater than 100 observations). A histogram can also aid in the detection of outliers (strange observations) or gaps in the data.
A histograph, also known as a frequency polygon, is a graph made by connecting the midpoints of histogram column tops. These graphs are exclusively used to portray data from the continuous variables displayed on a histogram.
A histograph smoothes out any sudden shifts in a histogram and is beneficial for displaying the continuity of the variable being analysed.
Frequency Polygon
Line-chart based on a histogram, it is drawn by joining the mid-points of the blocks at their apexes with a straight line. The extreme points of the line are joined to the horizontal (‘X’) axis (where the mid-point of the respective next class would have been) to result into a polygon. In a very large set of data (where the number of classes increases and difference between their widths decreases) the polygon turns into a smooth curve known as frequency curve or frequency distribution curve. Histographs (and histograms) are commonly used where the subject item is discrete (such as the number of students in a school) instead of being continuous (such as the variations in their heights).
Sometimes referred to as a frequency polygon, a histograph is usually preferred over a histogram where the number of classes is eight or more.
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This glossary post was last updated: 7th January, 2022 | 0 Views.