Box and Whisker Plot | Descriptive Statistics | Statistics and Data Analysis

Box and Whisker Plot | Descriptive Statistics | Statistics and Data Analysis

BOX PLOT
A box plot (also called a box-and-whisker plot) is another way of looking at a data set in an effort to determine its central tendency, spread, skewness, and the existence of outliers.

A box plot is a set of five summary measures of the distribution of the data:
►The median of the data,
►The lower quartile,
►The upper quartile,
►The smallest observation, and
►The largest observation.

The hinges of the box are the upper and lower quartiles (the rightmost and leftmost sides of the box). The median is marked as a vertical line across the box. The whiskers of the box plot are the extended lines from the upper and lower hinges to the largest and smallest observations, called the upper and lower whiskers. The largest and smallest observations must be within a distance of 1.5 times the interquartile range from the appropriate hinge or the quartile. The interquartile range (IQR) is the distance from the upper quartile to the lower quartile (the length of the box from hinge to hinge):
Mathematically IQR = Upper Quartile (QU) – Lower Quartile (QL)

Interquartile Range
Interquartile range means half the data are within the box. The points at a distance of 1.5 times of interquartile range above the upper quartile and below the lower quartile are inner fences. The whiskers are extended to the largest or smallest observation that is at a distance less than or equal to 1.5 times the interquartile range from the hinge. So that the smallest data point couldn't lie below the inner fence, and the largest data point couldn't lie above the inner fence. If one or more observations are farther away than that distance, they are marked as suspected outliers. The points at a distance of 3 times of interquartile range above or below the appropriate hinge are outer fences. The observations are at a distance of over 3 times the interquartile range from the appropriate hinge and are marked as outliers.

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