In general, values that fall outside of the adjacent value region are deemed outliers. Therefore, the upper adjacent value is 128, because 128 is the highest observation still inside the region defined by the upper bound of 131. Therefore, in this case, the lower adjacent value turns out to be the same as the minimum value, 68, because 68 is the lowest observation still inside the region defined by the lower bound of 67. In this example, the lower limit is calculated as \(Q1-1.5\times IQR=91-1.5(16)=67\). The adjacent values are defined as the lowest and highest observations that are still inside the region defined by the following limits: For a modified box plot, the whiskers are the lines that extend from the left and right of the box to the adjacent values. In a modified box plot, the box is drawn just as in a standard box plot, but the whiskers are defined differently. How come Minitab's box plot looks different than our box plot? Well, by default, Minitab creates what is called a modified box plot. Note, for example, that the horizontal length of the box is the interquartile range IQR, the left whisker represents the first quarter of the data, and the right whisker represents the fourth quarter of the data. For the right whisker, draw a horizontal line from the maximum value to the midpoint of the right side of the box.ĭrawn as such, a box plot does a nice job of dividing the data graphically into fourths.For the left whisker, draw a horizontal line from the minimum value to the midpoint of the left side of the box.Draw a vertical line connecting the lower and upper horizontal lines of the box at the median \(m\).Above the axis, draw a rectangular box with the left side of the box at the first quartile \(q_1\) and the right side of the box at the third quartile \(q_3\).Draw a horizontal axis scaled to the data.Here are some general guidelines for drawing a box plot: One nice way of graphically depicting a data set's five-number summary is by way of a box plot (or box-and-whisker plot). These three percentiles, along with a data set's minimum and maximum values, make up what is called the five-number summary. "Box-and-Whisker Plot."įrom MathWorld-A Wolfram Web Resource.On the last page, we learned how to determine the first quartile, the median, and the third quartile for a sample of data. On Wolfram|Alpha Box-and-Whisker Plot Cite this as: "Box-and-Whisker Plots." §2C in Exploratoryĭata Analysis. "Box Plot." §1.3.3.7 in NIST/ SEMATECH e-Handbook of Statistical can 56 things make a tetrahedral shape?.Values" (values closest to but still inside the inner fences). Separately and whiskers are dashed, ending with dashed crossbars at " adjacent Tukey also considered an additional variation in which the outliers are indicated Values and identifying the outliers with explicit labels (Tukey 1977, p. 41). Strip at the minimum, as illustrated above (left figure Tukey 1977, p. 40).Ī variation extended the whiskers only out to some arbitrary minimum and maximum In addition, Tukey's originalįormulation lacked horizontal crossbars, extended the whiskers all the way to theĮxtreme data points, and drew an unfilled dot at the maximum and a hatched horizontal In Tukey's original definition, the closely-related and lesser known hinges and were used instead of and (Tukey 1977, p. 39). Box-and-whisker plots areĪ number of other slightly different conventions are sometimes used. Them side by side (Gonick and Smith 1993, p. 21). Then, for every point more than 3/2 times the interquartile Points that are not outliers (i.e., that are within 3/2 times the interquartile Now extend the "whiskers" to the farthest Draw the statisticalĪs a horizontal line in the box. Plot, draw a box with ends at the quartiles and. A box-and-whisker plot (sometimes called simply a box plot) is a histogram-like method of displaying data, invented by J. Tukey.
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