4.v Measures of dispersion
4.v.2 Visualizing the box and whisker plot

Text begins

The box and whisker plot, sometimes simply called the box plot, is a type of graph that help visualize the five-number summary. It doesn't show the distribution in as much detail as histogram does, just it'south peculiarly useful for indicating whether a distribution is skewed and whether at that place are potential unusual observations (outliers) in the data set up. A box plot is platonic for comparing distributions because the eye, spread and overall range are immediately credible.

Figure 4.5.2.one shows how to build the box and whisker plot from the v-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.v.two.i

The effigy 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 fifty% of the data is found.
  • The vertical line that split the box in two is the median. Sometimes, the mean is also indicated by a dot or a cross on the box plot.
  • The whiskers are the two lines outside the box, that go from the minimum to the lower quartile (the start 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 (not shown on effigy 4.5.2.ane).
  • The box and whisker plot can be presented horizontally, like in figure 4.5.two.1, or vertically.

A variation of the box and whisker plot restricts the length of the whiskers to a maximum of 1.5 times the interquartile range. That is, the whisker reaches the value that is the furthest from the centre while still existence inside a distance of one.5 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.

Example 1 – Comparing of three box and whisker plots

The iii box and whisker plots of chart 4.5.two.i accept been created using R software. What can yous say nearly the iii distributions?

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

Data tabular array for Chart 4.5.two.1 
Information table for chart 4.v.2.1
Table summary
This table displays the results of Data table for chart 4.five.2.i. The information is grouped by Measurement (appearing every bit row headers), Distribution A, Distribution B and Distribution C (appearing as cavalcade headers).
Measurement Distribution A Distribution B Distribution C
Minimum 0.00 0.11 0.fourteen
Lower quartile (Q1) 0.02 0.37 0.69
Median (Q2) 0.11 0.48 0.88
Upper quartile (Q3) 0.32 0.58 0.95
Maximum 0.86 0.93 1.00
  • The centre of distribution A is the lowest of the 3 distributions (median is 0.11). The distribution is positively skewed, considering the whisker and half-box are longer on the correct side of the median than on the left side.
  • Distribution B is approximately symmetric, considering both half-boxes are near the aforementioned length (0.11 on the left side and 0.10 on the right side). It's the most full-bodied distribution considering 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 three 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 right side.

All three distributions include potential outliers. Permit'southward take distribution A, for example. The interquartile range is Q3 - Q1 = 0.32 – 0.02 = 0.thirty. Co-ordinate to the definition used by the function in R software, all values higher than Q3 + 1.five ten (Q3 - Q1) = 0.32 + 1.5 x 0.thirty = 0.77 are exterior the right whisker and indicated by a circumvolve. There are two potential outliers in distribution A.


Report a trouble on this folio

Is something not working? Is at that place information outdated? Can't find what you're looking for?

Please contact u.s. and let us know how we can help yous.

Privacy observe

Date modified: