They are commonly used to compare multiple sets of data simultaneously. The box plot for the above data set is shown below:īox plots are used to quickly get a sense of the distribution of data. These lines are the whiskers of the box plot. Draw lines from both ends of the IQR to their respective extrema. Connect the three middle points such that they form a rectangle. Once the five number summary is calculated, make points for each value in their corresponding positions over a number line:ģ. In this case, Q3 is between the 10th and 11th elements, which are 16 and 18, respectively. Q3 is the middle number between the median and the maximum.In this case, Q1 is between the 3rd and 4th elements, which are 4 and 5, respectively. Q1 is the middle number between the minimum and the median.If there are an even number of values, find the average of the two middle values. If there are an odd number of values, the median is the middle-most value. Q2, or the median is the middle value.Find Q1, Q2, Q3, the minimum, and the maximum. Use the following data set as a reference.ġ. Note that the elements in a set of data must be ordered from least to greatest to determine the values in the five number summary. How to construct a box plotĬonstructing a box plot involves determining each value in the five number summary. Because of how compact box plots are, they are also useful for comparing a large number of observations as well as for simultaneously comparing multiple data sets. For example, in addition to providing a five number summary, box plots also enable us to quickly determine whether the data is skewed, how tightly the data is grouped, and whether it has any outliers. Also, the "whisker" in the box and whisker plot refers to the lines between the minimum and Q1, and Q3 and the maximum.Īlthough box plots may not provide as much detail as other methods of displaying data, such as a histogram, box plots are useful in that the information they do provide is presented in a manner that is compact and can be interpreted quickly. The above would still apply except that "left" would refer to the bottom of the plot while "right" would refer to the upper part of the plot. Note that box plots can also be oriented vertically, by rotating the plot counter-clockwise. Maximum - largest value in the set it is the right-most point of the plot.On a box plot, Q3 is the right side of the box.
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