Identifying Outliers with Tukey’s Fences in Boxplot

Tukey’s Fences in Boxplot

Tukey’s fences, also known as Tukey’s hinges, are a method used in statistics to identify outliers in a dataset. In the context of boxplots, Tukey’s fences are used to determine the whiskers of the boxplot – the lines that extend from the box to indicate the range of typical values in the data. By using Tukey’s fences, we can visually represent and identify any potential outliers that fall outside of this range.

To calculate Tukey’s fences, we first need to find the interquartile range (IQR) of our dataset. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). Once we have calculated the IQR, we can then determine our upper and lower fences using the following formulas:

• Upper fence: Q3 + 1.5 * IQR

• Lower fence: Q1 – 1.5 * IQR

Any data points that fall above or below these fences are considered outliers and can be represented as individual points on a boxplot outside of the whiskers non-numeric argument to binary operator in r.

Examples in Different Programming Languages:

Python:

import numpy as np

# Generate some random data

data = np.random.normal(0, 1, 100)

# Calculate Q1, Q3, and IQR

q1 = np.percentile(data, 25)

q3 = np.percentile(data, 75)

iqr = q3 - q1

# Calculate Tukey's Fences

upper_fence = q3 + 1.5 * iqr

lower_fence = q1 - 1.5 * iqr

print("Upper Fence:", upper_fence)

print("Lower Fence:", lower_fence)

R:

set.seed(123)

# Generate some random data

data <- rnorm(100)

# Calculate Q1, Q3, and IQR

q1 <- quantile(data)[2]

q3 <- quantile(data)[4]

iqr <- q3 - q1

# Calculate Tukey's Fences

upper_fence <- q3 + 1.5 * iqr

lower_fence <- q1 - 1.5 * iqr

cat("Upper Fence:", upper_fence)

cat("\n")

cat("Lower Fence:", lower_fence)

By calculating Tukey’s fences in our datasets before creating boxplots or other visualizations like histograms or scatter plots will help us better understand our data distribution by identifying any potential outliers that may skew our analysis.