![]() We usually give the five-number summary in a table, and we can easily gather all of this information from a box-plot. The five-number summary, also called the five-figure summary, for any set of data will include the minimum and maximum values, the median, and ?Q1? and ?Q3? for the data set. In a box-and-whisker plot, the middle ?50\%? of the data is represented inside the box, the lowest ?25\%? in the whisker on the left, and the highest ?25\%? in the whisker on the right.Īs far as our quarters, this means that the first quarter is represented by the whisker on the left, the second quarter is represented by the part of the box to the left of the median, the third quarter is represented by the part of the box to the right of the median, and the fourth quarter is represented by the whisker on the right. ?25\%? of the data points lie between ?13? and ?14? ?25\%? of the data points lie between ?11? and ?13? ?25\%? of the data points lie between ?5? and ?11? ?25\%? of the data points lie between ?2? and ?5? In a box-and-whisker plot, the left end of the box represents ?Q1?, the median represents ?Q2?, and the right end of the box represents ?Q_3?. The third quartile, ?Q_3?, separates the third ?25\%? of data points from the upper ?25%? of data points. The second quartile, ?Q2?, is the median, and it separates the data set into halves. The first quartile, ?Q1?, separates the lowest ?25\%? of data points from the second ?25\%?. A quartile is a number that divides the data set into quarters. The box-and-whisker plot also shows us where each quartile of the data is located. Since the box above extends from ?5? to ?13?, the IQR is ?13-5=8?. So in this plot, we can say that the minimum is ?2?, that the maximum is ?14?, and so we know right away that the range of the data is ?14-2=12?. The dot at the end of the left whisker is the minimum of the data set, and the dot at the end of the right whisker is the maximum of the data set. Thus, the observations with values of 1.1 and 23.5 are both labeled as outliers in the box plot since they lie outside of the lower and upper boundaries. ![]() The vertical line inside the box is the median of the data set, so the median of the data set represented in the plot above is ?11?. The whiskers for the minimum and maximum values in the box plot are placed at 2.85 and 23.25. ![]() That is, if a data point is below Q1 1.5×IQR or above Q3 + 1.5×IQR, it is viewed as being too far from the central values to be reasonable. An outlier is any value that lies more than one and a half times the length of the box from either end of the box. The interquartile range is also just a simple calculation. The IQR is the length of the box in your box-and-whisker plot. The great thing about a box plot is that we know the median, range, upper and lower bounds just by looking at it. The big rectangle in the center is the box, and the little lines extending out from the sides are the whiskers. ![]()
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