4.five Measures of dispersion
4.5.2 Visualizing the box and whisker plot

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The box and whisker plot, sometimes but called the box plot, is a blazon of graph that assist visualize the five-number summary. Information technology doesn't bear witness the distribution in as much detail as histogram does, but information technology's especially useful for indicating whether a distribution is skewed and whether at that place are potential unusual observations (outliers) in the data set. A box plot is ideal for comparison distributions because the centre, spread and overall range are immediately apparent.

Figure four.5.2.ane shows how to build the box and whisker plot from the five-number summary.

Figure 4.5.2.1 shows how to build the box and whisker plot from the five-number summary

Description for Figure 4.5.2.1

The figure shows the shape of a box and whisker plot and the position of the minimum, lower quartile, median, upper quartile and maximum.

In a box and whisker plot:

  • The left and right sides of the box are the lower and upper quartiles. The box covers the interquartile interval, where l% of the data is found.
  • The vertical line that split the box in two is the median. Sometimes, the mean is as well indicated by a dot or a cross on the box plot.
  • The whiskers are the two lines exterior the box, that go from the minimum to the lower quartile (the beginning of the box) and then from the upper quartile (the stop of the box) to the maximum.
  • The graph is usually presented with an axis that indicates the values (non shown on figure 4.5.two.1).
  • The box and whisker plot can exist presented horizontally, like in effigy 4.5.2.1, or vertically.

A variation of the box and whisker plot restricts the length of the whiskers to a maximum of 1.v times the interquartile range. That is, the whisker reaches the value that is the furthest from the centre while all the same existence inside a distance of 1.five times the interquartile range from the lower or upper quartile. Data points that are outside this interval are represented as points on the graph and considered potential outliers.

Case 1 – Comparison of three box and whisker plots

The three box and whisker plots of chart 4.5.2.1 have been created using R software. What can you say about the three distributions?

Chart 4.5.2.1 Box and whisker plots and five-number summaries of distributions A, B and C

Data table for Chart 4.5.2.1 
Data table for nautical chart iv.5.2.ane
Tabular array summary
This tabular array displays the results of Data table for chart 4.5.ii.1. The data is grouped by Measurement (actualization as row headers), Distribution A, Distribution B and Distribution C (appearing as column headers).
Measurement Distribution A Distribution B Distribution C
Minimum 0.00 0.11 0.14
Lower quartile (Q1) 0.02 0.37 0.69
Median (Q2) 0.eleven 0.48 0.88
Upper quartile (Q3) 0.32 0.58 0.95
Maximum 0.86 0.93 1.00
  • The center of distribution A is the everyman of the iii distributions (median is 0.eleven). The distribution is positively skewed, because the whisker and half-box are longer on the correct side of the median than on the left side.
  • Distribution B is approximately symmetric, because both half-boxes are most the same length (0.11 on the left side and 0.10 on the correct side). It's the most full-bodied distribution because the interquartile range is 0.21, compared to 0.30 for distribution A and 0.26 for distribution C.
  • The centre of distribution C is the highest of the iii distributions (median is 0.88). The distribution C is negatively skewed because the whisker and half-box are longer on the left side of the median than on the correct side.

All three distributions include potential outliers. Allow's take distribution A, for example. The interquartile range is Q3 - Q1 = 0.32 – 0.02 = 0.30. According to the definition used by the role in R software, all values higher than Q3 + 1.5 x (Q3 - Q1) = 0.32 + i.v 10 0.30 = 0.77 are outside the right whisker and indicated past a circle. There are two potential outliers in distribution A.


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