Statistical Analysis of Student Test Data with NumPy & Matplotlib

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This document details a statistical analysis of simulated student test data using Python's NumPy and Matplotlib libraries. It includes the complete source code, a step-by-step guide on how to run the code, a detailed explanation of the code's functionality, and additional notes on interpretation and potential extensions.


student_analysis.py


 


import numpy as np
import matplotlib.pyplot as plt

# Set a seed for reproducibility
np.random.seed(42)

# Number of students
num_students = 200

# Simulate test scores (range 0-100)
test_scores = np.random.randint(40, 100, size=num_students)

# Simulate hours studied (range 0-20)
hours_studied = np.random.randint(0, 21, size=num_students)

# Simulate anxiety levels (range 1-10)
anxiety_levels = np.random.randint(1, 11, size=num_students)

# Calculate the mean test score
mean_test_score = np.mean(test_scores)

# Calculate the standard deviation of test scores
std_test_score = np.std(test_scores)

# Calculate the mean hours studied
mean_hours_studied = np.mean(hours_studied)

# Calculate the standard deviation of hours studied
std_hours_studied = np.std(hours_studied)

# Calculate the mean anxiety level
mean_anxiety_level = np.mean(anxiety_levels)

# Calculate the standard deviation of anxiety levels
std_anxiety_level = np.std(anxiety_levels)

# Calculate the correlation coefficient between hours studied and test scores
correlation_hours_test = np.corrcoef(hours_studied, test_scores)[0, 1]

# Calculate the correlation coefficient between anxiety levels and test scores
correlation_anxiety_test = np.corrcoef(anxiety_levels, test_scores)[0, 1]

# Define a threshold for high anxiety (e.g., anxiety level > 7)
high_anxiety_threshold = 7

# Define a threshold for low score (e.g., test score < 60)
low_score_threshold = 60

# Identify students with high anxiety and low scores
high_anxiety_low_score_students = np.where((anxiety_levels > high_anxiety_threshold) & (test_scores < low_score_threshold))

# Create a histogram of test scores
plt.hist(test_scores, bins=10, edgecolor='black')
plt.xlabel("Test Score")
plt.ylabel("Frequency")
plt.title("Distribution of Test Scores")
plt.show()

# Print the results
print("Descriptive Statistics:")
print("Mean Test Score:", mean_test_score)
print("Standard Deviation of Test Score:", std_test_score)
print("Mean Hours Studied:", mean_hours_studied)
print("Standard Deviation of Hours Studied:", std_hours_studied)
print("Mean Anxiety Level:", mean_anxiety_level)
print("Standard Deviation of Anxiety Level:", std_anxiety_level)

print("\nCorrelation Analysis:")
print("Correlation between Hours Studied and Test Score:", correlation_hours_test)
print("Correlation between Anxiety Level and Test Score:", correlation_anxiety_test)

print("\nStudents with High Anxiety and Low Scores:")
print("Number of students:", len(high_anxiety_low_score_students[0]))
print("Indices:", high_anxiety_low_score_students[0])
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2. How to Run the Code:

  1. Install Python: Ensure you have Python installed on your system (version 3.6 or higher is recommended).
  2. Install Libraries: Open a terminal or command prompt and install the necessary libraries using pip:


pip install numpy matplotlib
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  1. Save the Code: Save the code above as a Python file (e.g., student_analysis.py).
  2. Run the Script: Open a terminal or command prompt, navigate to the directory where you saved the file, and run the script using:


python student_analysis.py
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The script will print the statistical results to the console and display a histogram of the test scores in a separate window.

3. Source Code Explanation:

  • Import Libraries: import numpy as np and import matplotlib.pyplot as plt import the NumPy and Matplotlib libraries, respectively, and assign them aliases for easier use.
  • Set Random Seed: np.random.seed(42) sets the random seed to 42. This ensures that the random numbers generated are the same each time the script is run, making the results reproducible.
  • Data Simulation: The code simulates data for 200 students, including test scores, hours studied, and anxiety levels, using np.random.randint. The size parameter specifies the number of random numbers to generate.
  • Descriptive Statistics: np.mean() calculates the average value of each variable. np.std() calculates the standard deviation, which measures the spread of the data.
  • Correlation Analysis: np.corrcoef() calculates the correlation coefficient matrix. The element at [0, 1] of the matrix represents the correlation coefficient between the two input variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates a weak or no linear correlation.
  • Identifying Outliers: The code defines thresholds for high anxiety and low scores and uses np.where() to identify students who meet both criteria. np.where() returns the indices of the elements that satisfy the condition.
  • Histogram Generation: plt.hist() creates a histogram of the test scores. bins specifies the number of bins in the histogram. edgecolor='black' adds black borders to the bars. plt.xlabel(), plt.ylabel(), and plt.title() set the labels and title of the histogram. plt.show() displays the histogram.
  • Printing Results: The code prints the calculated statistics and the list of students with high anxiety and low scores to the console.

4. Additional Notes & Potential Extensions:

  • Data Source: In a real-world scenario, the data would come from a database, CSV file, or other data source. You would need to load the data into NumPy arrays using functions like np.loadtxt() or np.genfromtxt().
  • Data Cleaning: Real-world data often contains missing values or errors. You would need to clean the data before performing the analysis.
  • Statistical Significance: The correlation coefficients calculated in this script do not indicate statistical significance. To determine whether the correlations are statistically significant, you would need to perform a hypothesis test (e.g., a t-test).
  • Regression Analysis: You could use regression analysis to predict test scores based on hours studied and anxiety levels. This would allow you to quantify the relationship between these variables and test scores.
  • Visualization: You could create more sophisticated visualizations, such as scatter plots, box plots, and violin plots, to explore the data in more detail.
  • Grouping and Subsetting: You could analyze the data for different subgroups of students (e.g., by gender, grade level, or socioeconomic status).
  • More Variables: Adding more variables (e.g., attendance, prior academic performance) could provide a more comprehensive understanding of student performance.
  • Outlier Handling: Instead of simply identifying outliers, you could investigate the reasons for their existence and consider removing them from the analysis if appropriate.

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