![]() A picture is worth a thousand wordsĪlmost anyone, regardless of organizational level or education can understand and be able to answer questions about a box plot. It does not substitute for a more rigorous statistical comparison. This allows for a quick and simple visual comparison and directional indicator. When displayed on a single graph, different box plots can be compared with respect to the location of the median, amount of variation, skewness, and outliers. Easy comparison of different sets of data The box plot shows the central tendency (median line), variation (IQR), shape (relative length of the whiskers), and outliers. Here are some specific benefits of the box plot. Overall, the box plot provides a lot of information in a single easy-to-read graph. Were there any unexpected values for sales? Yes, there is an outlier on the low end of Product Line 4.Which product line seems to have a skewed distribution of sales? Product Line 1, since the whisker lengths are quite different.Which product line had the most variation? Product Line 2, since the width of the whiskers is the widest.Which product line had the least variation? Product Line 3, since the height of the box or the IQR is the smallest.Which product line had the highest median sales? Product Line 4, since the median line is the highest of the four.Here are some typical questions you might ask that can be answered by the box plot. Here is a box plot of sales by product line. Any values falling above or below the Upper and Lower Fences are plotted as outliers.īox plots are a valuable tool in comparing different data sets. Similarly, a distance of 1.5 times the IQR is laid out below the Q1 value, and a whisker is drawn to the lowest value falling below the Lower Fence. Your whisker is then drawn up to the largest value falling below the Upper Fence. If you multiply your IQR by 1.5 and add it to the Q3 value, you will have an assumed line called the Upper Fence, which is not drawn on the box plot. What does this mean? We will use the box plot below to explain it. In the definition of max and min above, it stated that these were the max and min values excluding outliers. Interquartile Range (IQR) : This is the range between the first and third quartiles.Whiskers : These are lines extending from the Q1 and Q3 values to the minimum and maximum values of your data set.Maximum Score (max): The highest value in your data set, excluding outliers.Or said another way, 25% of the data falls above this value. Upper Quartile (Q3): 75% of the scores fall below the upper or third quartile value.Half the values are greater than or equal to this value and half are less. Median: The median marks the physical center of the data and is shown by the line that divides the box into two parts.Lower Quartile (Q1): 25% of values fall below the lower or first quartile value.Minimum value (min): The lowest value in the data set, excluding outliers.Here are some definitions of the elements of the box plot. The plot can be either horizontal or vertical in orientation. ![]() The box is drawn from its first quartile (Q1) to its third quartile (Q3), with a horizontal line drawn in the middle representing the median. The lowest point is the minimum value of the data set and the highest point is the maximum value of the data set. John Tukey, an American mathematician and statistician.Ī box plot is constructed of two parts, a box and a set of whiskers as shown below. The box plot, also referred to as a box and whiskers plot, was introduced in 1970 by Dr. What if you were able to describe your data central tendency, variation, and shape and compare it to other processes all with one simple graph? We will describe how this can be done with a box plot.
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