 Mathematics

# Box and Whisker Plots Harry Stevens's image for:
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Image by: Box plots are an informative way to display a range of numerical data. It can show many things about a data set, like the lowest term in the set, the highest term in the set, the median, the upper quartile, and the lower quartile. Before I go into explaining what what I just said means, we must first delve into the history of a box plot. After, we do that, we will examine how to find all of the values that I mentioned above, as well as how to interpret one. Let us begin!

A box and whisker plot was first created by John Turkey. He was an American mathematician, and he invented this helpful method to display numerical data in the year 1977.

Now that we have covered the history of this important method of statistical representation, we must ask the question: "What does a box and whisker plot tell us?" These types of plots tell us the median, the upper and lower quartiles, the highest value of the data set, and the lowest value of the data set. You may have understood the last two things that I mentioned, but you may be questioning to yourself, "What do the first three things you said mean?" The first term is a measure of central tendency for the whole data set, and the latter two terms are measures of central tendency for different parts.

The median of a data set is the number that is in the middle when the data is placed in a row numerically. For example, if I had the data set 23. 14. 45, 34, 36, 40, and 75, in order to find the median, I would first have to arrange them in order. That would make the list become 14, 23, 34, 36, 40, 45, and 75. The number in the middle is 36, so that is the median of my data set. Not too difficult to understand, is it? Now let's move on to the upper and lower quartiles.

The upper quartile is simply a measure of central tendency for the higher part of the data set. Put simply, it is the median of the upper part of the numbers. For example, in the example above, the upper half of the data set is 40, 45. and 75 (excluding the median intentionally). With this new set of numbers, I can determine my upper quartile to be 45.

The lower quartile is also a measure of central tendency for half of the data set, but it is for the lower half of the data set. For the set above, the lower half of numbers would be 14. 23, and 34. Therefore, the lower quartile would be 23, as it is the median of the lower part of the numerical data set.

These three terms are three of the five components of a box and whisker plot.

Box plots are an informative way to display a range of numerical data. It can show many things about a data set, like the lowest term in the set, the highest term in the set, the median, the upper quartile, and the lower quartile. Before I go into explaining what what I just said means, we must first delve into the history of a box plot. After, we do that, we will examine how to find all of the values that I mentioned above, as well as how to interpret one. Let us begin!

A box and whisker plot was first created by John Turkey. He was an American mathematician, and he invented this helpful method to display numerical data in the year 1977.

Now that we have covered the history of this important method of statistical representation, we must ask the question: "What does a box and whisker plot tell us?" These types of plots tell us the median, the upper and lower quartiles, the highest value of the data set, and the lowest value of the data set. You may have understood the last two things that I mentioned, but you may be questioning to yourself, "What do the first three things you said mean?" The first term is a measure of central tendency for the whole data set, and the latter two terms are measures of central tendency for different parts.

The median of a data set is the number that is in the middle when the data is placed in a row numerically. For example, if I had the data set 23. 14. 45, 34, 36, 40, and 75, in order to find the median, I would first have to arrange them in order. That would make the list become 14, 23, 34, 36, 40, 45, and 75. The number in the middle is 36, so that is the median of my data set. Not too difficult to understand, is it? Now let's move on to the upper and lower quartiles.

The upper quartile is simply a measure of central tendency for the higher part of the data set. Put simply, it is the median of the upper part of the numbers. For example, in the example above, the upper half of the data set is 40, 45. and 75 (excluding the median intentionally). With this new set of numbers, I can determine my upper quartile to be 45.

The lower quartile is also a measure of central tendency for half of the data set, but it is for the lower half of the data set. For the set above, the lower half of numbers would be 14. 23, and 34. Therefore, the lower quartile would be 23, as it is the median of the lower part of the numerical data set.

These three terms are three of the five components of a box and whisker plot (the other two being the highest and lowest values in the data set. Once you find all five of these values, it is easy to draw a box and whisker plot. First, draw a number line that has a scale that would fit for your numbers. Second, draw a small vertical line at the median, the upper quartile, and lower quartile. Connect these three lines with two horizontal lines, one going on the top and one on the bottom. Once you have done that, place dots at the highest and lowest values of the data set. Connect the dots to the "box" you created with a horizontal line to the middle (these are your "whiskers"). Once you have followed these steps, you have created a box and whisker plot.

Box and whisker plots are an informative and easy-to-understand way to display and show people numerical data. We owe a lot of thanks to John Turkey, as he provided society with another incredible way to display one of the most important parts of mathematics: numbers.

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