Introduction to Density Plots

Density plots are a valuable tool in statistical analysis, providing a smooth representation of data distribution. They help visualize the probability density function of a continuous variable, making it easier to identify patterns, trends, and anomalies. In this article, we provide three practical examples of density plots to illustrate their diverse applications.

Example 1: Visualizing Student Test Scores

In educational settings, density plots can effectively illustrate the distribution of student test scores, helping educators identify performance trends.

In this example, let’s consider a dataset containing the final exam scores of 200 students across various subjects. A density plot can visually represent how scores are distributed—whether they cluster around certain values or are more uniformly spread.

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

# Generate synthetic exam scores data
np.random.seed(0)
exam_scores = np.random.normal(loc=75, scale=10, size=200)

# Create a density plot
sns.kdeplot(exam_scores, shade=True, color='blue')
plt.title('Density Plot of Student Exam Scores')
plt.xlabel('Exam Scores')
plt.ylabel('Density')
plt.grid()
plt.show()

This density plot shows a peak around 75, indicating that most students scored around this value. The spread is moderate, suggesting a variety of performance levels among students.

Notes:

• Variations: You can segment data by subject or demographic factors (e.g., age, gender) to compare distributions across groups.

Example 2: Analyzing Real Estate Prices

Density plots also serve as effective tools in the real estate market, helping analysts visualize the distribution of property prices in a given area.

Consider a dataset of house prices in a metropolitan region. A density plot can help determine price ranges where most transactions occur, providing insights for buyers and sellers alike.

import pandas as pd

# Sample real estate data
prices = pd.Series([300000, 450000, 250000, 700000, 550000, 300000, 800000, 200000, 400000, 600000])

# Create a density plot
sns.kdeplot(prices, shade=True, color='green')
plt.title('Density Plot of Real Estate Prices')
plt.xlabel('House Prices ($)')
plt.ylabel('Density')
plt.grid()
plt.show()

This plot reveals a significant concentration of prices between $300,000 and $600,000, indicating that most properties fall within this range. It also highlights the presence of higher-priced outliers.

Notes:

• Variations: Consider using logarithmic scales for highly skewed data to improve interpretability.

Example 3: Examining Environmental Data

Density plots can also analyze environmental data, such as air quality measurements across different locations and times.

In this case, let’s explore the distribution of PM2.5 levels recorded in urban areas over a month. This density plot can help identify pollution trends and periods of concern.

# Sample PM2.5 levels in micrograms per cubic meter
pm25_levels = np.random.normal(loc=35, scale=15, size=300)

# Create a density plot
sns.kdeplot(pm25_levels, shade=True, color='red')
plt.title('Density Plot of PM2.5 Levels')
plt.xlabel('PM2.5 Levels (µg/m³)')
plt.ylabel('Density')
plt.grid()
plt.show()

This density plot indicates that PM2.5 levels predominantly cluster around 35 µg/m³, with some variability suggesting occasional spikes, which may warrant further investigation.

Notes:

• Variations: Analyze variations over time by creating multiple density plots for different time periods to observe trends.

By utilizing these examples of density plot example, users can gain insights into various datasets, enhancing their understanding of data distributions in different contexts.