How to Make a Box Plot From a Cumulative Frequency

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A Box Plot is a graph used in statistics that shows 50 percent of the data set as a box. Box plots are useful to observe data from a frequency distribution, its mean values, extreme values and the variability of data. Box Plots are useful because they show how a data set is spread, shows if there is symmetry on the data set and, most importantly, box plots show outliers, which are absent from most statistical graphs.

    Find out the Quartiles of your data set. There are 3 quartiles on your data set, quartiles divide your data set in increments of 25%. The second quartile is the mean of your data set (50 percent) The first quartile is the mean of the first half of your data set (25 percent) The third quartile is the mean of the second half of your data set (75 percent) Find the maximum, and minimum of your frequency distribution. These five points will define your boxplot.

    Draw an XY diagram. Label the Y axis (vertical) with the values of the frequency distribution. Label the X axis (horizontal) with the data label for the frequency distribution.

    Place your quartiles, minimum and maximum points on the diagram, on the same column. Draw a box from the first quartile to the third quartile. Draw a horizontal line that passes through the second quartile, dividing the the box in two.

    Draw a vertical line that connects all the quartile, minimum and maximum points. Place points for outliers (if any).

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