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Chapter 5: Measures of Relative Standing Back To Chapter

5.9: Modified Boxplots

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Modified Boxplots

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5.8: What Are Outliers?

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Recall that a data set can be represented using a five-number summary and visualized using a boxplot having a minimum value, first quartile, second quartile, third quartile, and the maximum value.

The box plot is slightly altered to produce a modified box plot that provides more visual insights into the location of outliers and the spread of data from the center.

First, subtract 1.5 times IQR from Q₁ and add 1.5 times IQR to Q₃ to obtain the new minimum and maximum values. Values beyond these limits are considered outliers and marked with an asterisk.

Now modify the whiskers to join only those values within the range of 1.5 times IQR.

This generates a modified box plot with clearly identified outliers.

5.9: Modified Boxplots

A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.

However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.

Initially, we calculate the adjusted minimum and maximum values to construct the modified boxplot. The modified minimum value equals the value of Q₁ minus the interquartile range multiplied by 1.5. Next, we can calculate the modified maximum value. It is equal to the value of Q₃ plus the value of the interquartile range multiplied by 1.5.

Now, the whiskers of the standard box plot are modified. The whiskers are shorter, and the edges of the whiskers lie at the adjusted minimum and maximum values. Further, all the values beyond the modified minimum and maximum values are considered outliers and are marked with an asterisk.

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Modified Boxplots Spread Of Data Outliers Box And Whisker Plot Quartile Values Median Value Interquartile Range Adjusted Minimum Value Adjusted Maximum Value Whiskers Visualizing Data Spread Asterisk

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