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 qu…
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.
Q1: How do you calculate the adjusted minimum and maximum values for a modified boxplot?
The adjusted minimum equals Q1 minus 1.5 times the interquartile range (IQR). The adjusted maximum equals Q3 plus 1.5 times the IQR. These calculated values replace the standard minimum and maximum, creating boundaries that help identify outliers beyond the typical data spread.
Q2: What is the main difference between a standard boxplot and a modified boxplot?
A standard boxplot displays the five-number summary but doesn't identify outliers. A modified boxplot uses adjusted minimum and maximum values based on the IQR to clearly mark values beyond these limits as outliers with asterisks, providing better visual insight into data distribution and what are outliers.
Q3: How are whiskers modified in a modified boxplot compared to a standard boxplot?
In a modified boxplot, whiskers are shortened and repositioned to extend only to the adjusted minimum and maximum values calculated using the 1.5 times IQR formula. This contrasts with standard boxplots where whiskers extend to the actual minimum and maximum data values.
Q4: Why is the 1.5 times IQR rule used to identify outliers in modified boxplots?
The 1.5 times IQR rule establishes a consistent statistical boundary for detecting unusual values that deviate significantly from the central data cluster. Values falling outside this range are marked with asterisks, making outliers visually distinct and helping analysts recognize extreme or anomalous data points.
Q5: What information does a modified boxplot reveal that a standard boxplot does not?
A modified boxplot explicitly identifies and marks outliers with asterisks, showing which values lie far from the center. It also visualizes the actual spread of typical data by adjusting whisker positions, providing clearer insight into data distribution patterns and the presence of extreme values.
Q6: How do you determine if a data value is an outlier using the modified boxplot method?
A value is classified as an outlier if it falls below the adjusted minimum (Q1 minus 1.5 times IQR) or above the adjusted maximum (Q3 plus 1.5 times IQR). These outliers are plotted individually with asterisks rather than included within the whisker range.
Q7: What role does the interquartile range play in constructing a modified boxplot?
The interquartile range (IQR) is the foundation for calculating adjusted boundaries in a modified boxplot. Multiplying the IQR by 1.5 and adding or subtracting from Q3 and Q1 respectively determines the whisker endpoints and defines which values qualify as outliers.