![]() ![]() The lower fence is defined by the following formula: The lower fenceĪny data value smaller than the lwoer fence will be considered an outlier. Instead it will be marked with a asterisk or other symbol. The idea is that anything outside the fences is a potential outlier and shouldn’t be included in the main group that we graph. With boxplots, this is done using something called “fences”. As you study statistics, you will see that different settings will use different techniques to flag or mark a potential outlier. Other than “a unique value”, there is not ONE definition across statistics that is used to find an outlier. The video below shows you how to get to that menu on the TI84:įor this data set, you will get the following output: While these numbers can also be calculated by hand (here is how to calculate the median by hand for instance), they can quickly be found on a TI83 or 84 calculator under 1-varstats. The five number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value. Steps to Making Your Box plot Step 1: Calculate the five number summary for your data set Let’s suppose this data set represents the salaries (in thousands) of a random sample of employees at a small company. To review the steps, we will use the data set below. Like a histogram, box plots ignore information about each individual data value and instead show the overall pattern. One of the more common options is the histogram, but there are also dotplots, stem and leaf plots, and as we are reviewing here – boxplots (which are sometimes called box and whisker plots). There are many possible graphs that one can use to do this. Remember, the goal of any graph is to summarize a data set. In the following lesson, we will look at the steps needed to sketch boxplots from a given data set. ![]() This way, you will be very comfortable with understanding the output from a computer or your calculator. However, when you are first learning about box plots, it can be helpful to learn how to sketch them by hand. The figure below summarizes all three cases.Typically, statisticians are going to use software to help them look at data using a box plot. ![]() If there are individual data points plotted, the whiskers indicate the largest/lowest points inside the range defined by 1st or 3rd quartile plus 1.5 times IQR. In summary, if there are no individual data points plotted, the whiskers indicate data’s minimum and maximum. Because the point is outside of that range, it would often be considered an outlier. The computer will plot the point that is outside of the 3rd quartile plus 1.5 times IQR range. The quartiles are all the same, but the largest value no greater than 19 is 12. Thus the upper whisker will reach to 19.įinally, suppose that the last observation is 20 instead of 19, so the data looks like this: (1,1,4),(4,5,8),(8,9,10),(10,12, 20). The quartiles are all the same, but the largest value no greater than 19 is 19. The lower whisker is defined analogously. The largest value that is no greater than 19 is 13, so the upper whisker will reach to 13. In this case, the third quartile plus 1.5 times IQR is 10 + 1.5*6 = 19. The length of the upper whisker is the largest value that is no greater than the third quartile plus 1.5 times the interquartile range. The box in the box plot will show the median and the first and third quartiles. ![]() (I purposefully made the numbers at the border of each quartile equal so we don’t have to worry about calculating quartiles in a discontinuous distribution.) The first quartile is 4, median is 8 and the third quartile is 10, interquartile range (IQR) is 6. I grouped the observations into four equal groups so that we can easily spot the quartiles. ![]()
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