A box and whisker plot also called a box plot-display the five number summary of a set of data. It is a useful visual device for communicating the information contained in a data set in the box-whisker plot. The construction of a box-and-whisker plot makes use of the quartiles of data set and may be accomplished by following these five steps:
- Represent the variable of interest on the horizontal axis.
- Draw a box in the space above the horizontal axis in such a way that left end of the box aligns with the first quartile Q1 and the right end of the box aligns with the third quartile Q3.
- Divide the box into two parts by a vertical line that aligns with the median Q2.
- Draw a horizontal line called a whisker from the left end of the box to a point that aligns with the smallest measurement in the data set.
- Draw another horizontal line, or whisker, from the right end of the box to a point that aligns with the largest measurement in the data set.
Examination of a box-and-whisker plot for a set of data reveals information regarding the amount of spread, location of concentration, and symmetry of the data. The box plot is a graphical representation of a data set that gives a visual impression of location, spread, and the degree and direction of skewness. It also allows for the identification of outliers.
A box plot consists of the following:
- A central box extends from the 25th to the 75th percentiles. At the median value of data set the box is divided into two compartments. The relative sizes of the two halves of the box provide an indication of the distribution symmetry. If they are approximately equal, the data set is roughly symmetric; otherwise, we are able to see the degree and direction of skewness.
- The line segments projecting out from the box extend in both directions to the adjacent values. The adjacent values are the points that are 1.5 times the length of the box beyond either quartile. All other data points outside this range are represented individually by little circles; these are considered to be outliers or extreme observations that are not typical of the rest of the data.
How to read a Box Plot: Steps
Below are given the steps on how to read a box plot, the typical Box and Whisker Plot is given in the diagram above.
Step 1: Find the minimum (Lower adjacent value); the minimum is the far left-hand side of the graph, at the tip of the whisker. For this graph, the left whisker end is at approximately 0.75.
Step 2: Find First Quartile, Q1; the first quartile is represented by the far left hand side of the box
Step 3: Find the median; the median is represented by the vertical bar.
Step 4: Find the third quartile, Q3; it is the far right hand edge of the box.
Step 5: Find the maximum (Upper adjacent value); the maximum is the right end of the whiskers.
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