Box-and-whisker Plots: Intro

Box-and-Whisker Plots Intro A box-and-whisker plot is a more advanced way of visualizing data. Your data is usually clustered around some central value; the “box” shows the middle half of these values. Here is an example of a box-and-whisker plot:

Notice there is a few measures we have to calculate in order to draw our plot. To make matters more manageable, let’s create a series of steps to follow: 1) Order your data in numerical order (smallest to largest). 2) Find the median of your data (remember, your median is the “middle number” in your data). The median divides your data in two halves. 3) Find the lower and upper quartiles. To do this, find the median of each halve. 4) The lower extreme and upper extremes are the high and low values in your data. 5) Draw your plot.

Creating a box-and-whisker plot In this section, we will take a data set and create a box-and-whisker plot following the steps we outlined above. We will use the following data set:

10, 12, 14, 23, 24, 26, 36, 37, 41, 59

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Knowledge of data analysis and probability Interpret information from graphical representations (e.g., stem-leaf, box-whisker and scatter plots).

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24, 10, 12, 23, 37, 41, 26, 59, 36, 14 Step 1: Order your data in numerical order. 10, 12, 14, 23, 24, 26, 36, 37, 41, 59 Step 2: Find the median. The median is the middle number of a data set, therefore our median is 25. Remember, when finding the median, if you have an even number of values in a data set, find your two middle values and take their average. In this example, my middle numbers are 24 and 26 and if I take their average I get 25—which becomes my median. If you have an odd number of values in a data set, we simply find the middle number and that value becomes our median. Here’s a quick example,

1, 2, 3, 4 Since we have an even number of values, our median is the average of our two middle numbers: 2.5

1, 2, 3 Since we have an odd number of values, our median is simply the middle number: 2

Notice our median divides the data set into two halves: 10, 12, 14, 23, 24 and 26, 36, 37, 41, 59. Step 3: Find the median of each halve; these will become our lower and upper quartiles. The median of the lower halve, 10, 12, 14, 23, 24, is 14—therefore, our lower-quartile is 14. The median of the upper halve, 26, 36, 37, 41, 59, is 37—therefore, our upper-quartile is 37. Step 4: The lower and upper extremes are the largest and smallest values in our data set. In this example, the smallest value is 10—our lower extreme. The largest value is 59—our upper extreme. Step 5: Draw the plot. Now we can put all our values into your plot and draw our box-and-whiskers. Here’s what we have so far, Lower Extreme: 10 Upper Extreme: 59

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Lower Quartile: 14 Upper Quartile: 37

Median: 25

Knowledge of data analysis and probability Interpret information from graphical representations (e.g., stem-leaf, box-whisker and scatter plots).

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25

36 39

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45 48

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54 57

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59

Extra Example Create a box-and-whisker plot given the following data: 1, 4, 7, 18, 11, 14, 13, 3 1) Order your data set: 1, 3, 4, 7, 11, 13, 14, 18 2) Find your median: Since our data set has an even number of values, we find the average of our two middle values—7 and 11, which is 9. 3) Find the median of either halve, 1, 3, 4, 7: median is 3.5 11, 13, 14, 18: median is 13.5 4) Upper extreme is 18; lower extreme is 1 5) Draw plot,

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13.5

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In this example, I have drawn the box-and-whisker plot below the number line. I have also included the data points (in blue) on the number line to give you a better visual representation of where they land in relation you the plot (these are not necessary).

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Knowledge of data analysis and probability Interpret information from graphical representations (e.g., stem-leaf, box-whisker and scatter plots).

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