![]() This line right over here, the middle of the box, this tells us the median value, and we see that the median value here, this is 140,000 kilometers. While on the box plot, it explicitly, it directly tells me the median value. In Minitab's modified box plots, outliers are identified using asterisks. The histogram is not useful, because throwing all the values into these buckets. In this case, the IQs of 136 and 141 are greater than the upper adjacent value and are thus deemed as outliers. 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. On the last page, we learned how to determine the first quartile, the median, and the third quartile for a sample of data.
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