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Interpreting Box Plots In Data Science

Interpreting Box Plots In Data Science

Abhinav Agarwal's photo
Abhinav Agarwal
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4 min read

Box plots are a type of statistical graph that helps us visualize the distribution of data. They are a simple and effective way to compare the distributions of data from different groups.

A box plot is made up of five parts: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.

In this Blog Post, we will look At each of them separately and learn to interpret them.

Lets understand Each of the terms individually

  • Minimum: The smallest value in the data set.

  • First quartile (Q1): The middle value of the bottom half of the data set.

  • Median: The middle value of the entire data set.

  • Third quartile (Q3): The middle value of the top half of the data set.

  • Maximum: The largest value in the data set.

  • Interquartile range (IQR): The distance between Q1 and Q3.

  • Whiskers: The lines that extend from the box to the minimum and maximum values.

  • Outlier: A data point that falls outside the whiskers.

The box plot can be used to visualize the distribution of data and to identify outliers. It can also be used to compare the distributions of data from different groups.

Further analysis

The median is shown by the horizontal line in the box.
The dashed lines, referred to as whiskers, extend from the top and bottom of the box to indicate the range for the bulk of the data. Any data outside this range will be considered an outliers.

The rectangular box, i.e., Interquartile Range represents the range in which 50% of the data lies.

The region between q3 and Max Represents the region in which the top 25% of the data lies and the region between q1 and min represents the region in which the bottom 25% of the data lies.

The black lines, referred to as whiskers, extend from the left and right of the box to indicate the range for the bulk of the data

The median divides the into two equal parts. To the right of the median, lies the top 50 percent of the data, and to the left lies the bottom 50% of the data.

Any data outside of the whiskers is plotted as single points or circles (often considered outliers).

There are many variations of a boxplot; By default, the R function extends the whiskers to the furthest point beyond the box, except that it will not go beyond 1.5 times the IQR

Practical Implementation in Python

import matplotlib.pyplot as plt
import numpy.random as rnd

# Generate some random data
data = rnd.randn(100)

# Create a box plot of the data
plt.boxplot(data)
plt.show()

The code generates 100 random numbers from a standard normal distribution. The box plot shows the distribution of these numbers.

The following are the key features of thi box plot:

  • The median (middle value) is 0.

  • The interquartile range (IQR) is approximately 1.

  • There are no outliers.The advantages & disadvantages of using box plots over other statistical graphs

Box plots are a versatile tool that can be used to visualize the distribution of data in a variety of ways

Here are some of the advantages of using box plots over other statistical graphs:

  • They are easy to understand. Box plots are a simple and intuitive way to visualize data. They can be easily understood by people with no statistical training.

  • They can be used to compare the distributions of data from different groups. Box plots can be used to compare the distributions of data from different groups, such as different ages, genders, or treatment groups. This makes them a useful tool for data analysis and research.

  • They can be used to identify outliers. Outliers are data points that fall outside the normal range of values. Box plots can be used to identify outliers, which can be helpful for identifying potential problems with your data.

  • They are robust to outliers. Outliers can have a significant impact on the appearance of other statistical graphs, such as histograms and bar charts. However, box plots are less affected by outliers, making them a more reliable tool for data visualization.

Here are some of the disadvantages of using box plots:

  • They do not show the shape of the distribution of data. Box plots only show the median, quartiles, and outliers. They do not show the shape of the distribution of data, such as whether it is symmetrical or skewed.

  • They can be difficult to interpret for large data sets. Box plots can be difficult to interpret for large data sets. This is because the whiskers can become very long, making it difficult to see the actual data points.

Overall, box plots are a versatile and useful tool for visualizing the distribution of data. They are easy to understand, can be used to compare the distributions of data from different groups, and can be used to identify outliers. However, it is important to be aware of their limitations, such as their inability to show the shape of the distribution of data and their difficulty to interpret for large data sets.

Machine Learning