![]() ![]() 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. ![]() The interquartile range is not part of this five-number summary, but is useful alongside it as a measure of dispersion or spread.In essence, the five horizontal lines are all there is to it. This information can then be presented in a box plot (box and whisker diagram) making it easy to compare with other sets of data. The median and lower and upper quartiles, along with the minimum value and the maximum value of the data set, form a five-number summary of descriptive statistics for the data set. The IQR is far more representative of the spread of this data set because it is not affected by extreme values. The smaller the value for the interquartile range, the narrower the central 50\% of data for the data set. The larger the interquartile range, the wider the spread of the central 50\% of data. The interquartile range (IQR) is a descriptive statistic, and measures the variability or spread of the data. Note: the lower quartile is the median of the lower half of the data, the upper quartile is the median of the upper half of the data.įind the interquartile range of the following data. Interquartile range \bf th percentile as 75\% of the data lies below this value. Interquartile range is the difference between the upper quartile (or third quartile) and the lower quartile (or first quartile) in an ordered data set.
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