46 Box plot

46.1 Box plot

Box plots, also known as box-and-whisker plots, are a type of statistical graph that is used to display the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and maximum. They are particularly useful for identifying outliers and understanding the spread and skewness of the data.

Purpose:

Box plots (also known as box-and-whisker plots) are used to display the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. They are excellent for detecting outliers and understanding the spread and skewness of the data.
A box plot visualizes data distribution in a compact manner. The central box represents the middle 50% of the data (from Q1 to Q3). Inside the box, a line indicates the median of the data.
Whiskers extend from either side of the box to the smallest and largest values within 1.5 times the interquartile range (the distance between Q1 and Q3). Data points outside this range are considered outliers and are often plotted as individual points.

How Data Analysts Use Box Plots:

Identify Outliers: The whiskers extend from the hinges to the highest and lowest values that are within 1.5 * IQR (interquartile range, which is Q3 - Q1) from the quartiles, providing a quick visual cue about the presence of outliers beyond these bounds.

Compare Distributions: Analysts use box plots to compare the distributions across different categories or groups within a dataset, making it easy to see variations in medians, the ange of data, and overall variability.

Spot Asymmetry and Spread: Box plots allow analysts to easily see if the data is symmetrically distributed, skewed, or if one tail is longer than the other.

46.1.1 1. Creating Box Plots in R

R provides several libraries to create box plots, but the base installation already includes a function for this.

R Code:

Code

# Data
data <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105)

# Create a box plot
boxplot(data, main="Box Plot", ylab="Values", col="blue", border="orange")

This R script generates a box plot of the specified data. The plot includes a box and whiskers, which visually encapsulate the core distribution of the data, highlighting the median and potential outliers.

46.1.2 2. Creating Box Plots in Python

In Python, matplotlib is a versatile library used for creating box plots, but seaborn, which is built on top of matplotlib, provides a more high-level interface and better default visuals.

!pip install seaborn

Python Code:

Code

import matplotlib.pyplot as plt
import seaborn as sns

# Data
data = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105]

# Create a box plot
sns.boxplot(x=data)
plt.title("Box Plot")
plt.xlabel("Values")
plt.show()

This Python script uses seaborn to create a box plot, which automatically manages aesthetics and provides a more visually appealing plot compared to the basic matplotlib version.

46.1.3 Summary:

Box plots are a powerful tool for statistical analysis, allowing quick insights into the core tendencies and variability of data, as well as highlighting outliers. These plots are applicable in various fields, from finance to biomedical sciences, anywhere data distribution needs to be quickly and clearly visualized. Whether in R or Python, creating a box plot can help analysts and researchers efficiently communicate statistical findings.

End of Course. All the Best