![]() In particular, in that case, there may be many repetitions similar or equal to the median. If the box is " thin," the dataset is not spread too much.You can think of it as the middle of the dataset: half of the entries are larger and the other half smaller. The line going through the middle of the box is the median.To be precise, it's where around half of the entries are. The box marks the interquartile range.In other words, all entries of the dataset (no matter how many there are) fall somewhere between the two values. The two limit lines are the dataset's extrema.From the top, they are: the maximum, third quartile, median, first quartile, and minimum. The five horizontal lines on the graph mark the five-number summary of the dataset.Voilà! When you finish the last step, you can proclaim yourself a box-and-whisker plot maker, and the graph is ready! Once that's done, we connect their midpoints to the box's sides marking the third and first quartiles, respectively. We look for the maximum and minimum on the scale and draw lines in the corresponding places, again parallel to the quartiles. ![]() Next, we mark the median by a line inside the rectangle that is parallel to the quartiles. We mark the first and third quartiles on the line (note how Omni's box-and-whisker plot calculator draws the thing vertically with the scale to the left, but at times, you may come across a horizontal version) and draw a rectangle whose two opposite sides correspond to those values (the rectangle's width doesn't matter). To graph a box plot, we begin with the box itself. Once we have the five values, we can get the crayons ready: it's drawing time! In our case, the entries are ordered, so we have maximum = a n \textrm a ( n + 1 ) /2 appears in both the calculations). That is because it's usually easier to calculate the five numbers in the order given below. Also, note that below, the subsequent steps on how to make a box-and-whisker plot are in a different order to those in the above section. If they weren't, we'd have to order them before we do anything else. For simplicity, let's assume that they are listed from least to most. Say that you have a sequence of numbers a 1, a 2, …, a n a_1, a_2, \ldots, a_n a 1 , a 2 , …, a n . Therefore, explaining how to find them seems like a reasonable thing to begin with, don't you think? What is more, we'll also go through the whole thing the other way round, i.e., explain how to read a box-and-whisker plot.Īs mentioned in the above section, the box-and-whisker plot calculator is basically a tool to visualize five values associated with a dataset. For now, we'll focus on general instructions and formulas, which we then apply to a numerical example in the dedicated section. On the plot, it's the bottom dark blue line.Īlright, now that we know what a box plot is and can identify its components, it's time to see how to make a box-and-whisker plot in practice. The opposite of the maximum: it marks the smallest entry of the dataset. On the graph, it's the bottom side of the box. Together with the third quartile, it forms the interquartile range, i.e., the box on the box-and-whisker plot example above, which shows where roughly half of the entries are. Similar to its equivalent from point 2., it marks the end of the range in which one-fourth of the values lie. In the picture, it's the light blue line in the middle. It's not the same as the mean, mind you! Instead, it says that half of the entries are larger and the other half are smaller than the median. On the plot, it's the top side of the box. Formula-wise, it's the median of the top half of the values. As such, the third quartile marks the end of the range in which three-fourths of the entries lie. On the graph, it's the top dark blue line.Ī quartile is one-fourth of the dataset. Simple enough: it's the largest entry in the dataset. It's time to learn what they are from top to bottom. The bunch is called the five-number summary of a dataset, and sure enough, Omni's box-and-whisker plot maker provides their values together with the graph itself. In essence, the five horizontal lines are all there is to it.
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