A box plot (box-and-whisker plot) is a visualization used to depict the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The box plot provides insights into data distribution, central tendency, variability, and outliers.

Understanding how to find the range of a box plot involves identifying the whiskers’ endpoints, which typically represent the range of non-outlier data, and calculating the interquartile range (IQR). This guide explores how to determine these values in R Programming Language.

Creating a Box Plot in R

Before finding the range, let’s create a box plot. Consider a simple example with a set of data.

# Create a sample vector of data
data <- c(1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 22)
# Create a box plot
boxplot(data, main = "Box Plot Example", xlab = "Sample Data")

Output:

Find Range of Box Plot in

This code snippet creates a box plot with the default whisker range, usually 1.5 times the interquartile range (IQR) from the quartiles.

Finding the Range of a Box Plot

To find the range of a box plot, you need to identify the five-number summary, which includes:

1. Minimum: The smallest value not considered an outlier.
2. First Quartile (Q1): The 25th percentile of the data.
3. Median (Q2): The 50th percentile (middle value) of the data.
4. Third Quartile (Q3): The 75th percentile of the data.
5. Maximum: The largest value not considered an outlier.

You can extract these values and determine the whisker range using the boxplot.stats function in R:

# Get the box plot statistics
box_stats <- boxplot.stats(data)
# Display the five-number summary
print(box_stats$stats) 

Output:

[1]  1.0  4.0  7.5 14.0 22.0

Whisker Range

The whiskers in a box plot typically extend to 1.5 times the IQR from the quartiles. You can calculate this range to find the typical minimum and maximum values for the box plot:

# Calculate the interquartile range (IQR)
iqr <- box_stats$stats[4] - box_stats$stats[2]
# Calculate the lower whisker
lower_whisker <- box_stats$stats[2] - 1.5 * iqr
# Calculate the upper whisker
upper_whisker <- box_stats$stats[4] + 1.5 * iqr
cat("Lower whisker:", lower_whisker, "\n")
cat("Upper whisker:", upper_whisker, "\n")

Output:

Lower whisker: -11 

Upper whisker: 29

In addition to the whiskers, box plots can also display outliers. Outliers are data points outside the whisker range. To find these, you can use the out attribute from boxplot.stats:

# Get the outliers
outliers <- box_stats$out
print(outliers)  

Output:

numeric(0)

Summary

To find the range of a box plot in R:

• Create a box plot to visualize the data distribution.
• Use boxplot.stats to extract the five-number summary (minimum, Q1, median, Q3, maximum).
• Calculate the interquartile range (IQR) to determine the whiskers’ endpoints.
• Identify outliers as values outside the whisker range.

These methods allow you to understand the key characteristics of a box plot and determine the typical range of non-outlier data, providing insights into your data’s distribution and variability.