Calculate Variance of an Array with One-Pass Algorithm 📊

Overview

This repository contains a simple and efficient implementation of a one-pass algorithm to calculate the variance of an array. The variance is a key statistical measure that quantifies the dispersion of a set of data points. Understanding variance is crucial for data analysis, as it provides insight into how spread out the data is.

Key Features

• One-Pass Calculation: This algorithm computes variance in a single pass through the data, making it efficient in terms of time complexity.
• Unbiased Estimation: The implementation provides an unbiased estimate of the sample variance, ensuring accurate results.
• JavaScript Implementation: The code is written in JavaScript, making it easy to integrate into web applications or Node.js environments.

Topics Covered

• Array manipulation
• Deviation and dispersion
• JavaScript and Node.js programming
• Mathematical concepts related to statistics
• Sample variance and standard deviation calculations

Installation

To get started with the project, clone the repository:

bash git clone https://github.com/ayugacor/stats-array-variancetk.git cd stats-array-variancetk

Install the necessary dependencies if you are using Node.js:

bash npm install

Usage

To calculate the variance of an array, use the following function:

```javascript const { calculateVariance } = require('./variance');

const data = [10, 20, 30, 40, 50]; const variance = calculateVariance(data); console.log(Variance: ${variance}); ```

This will output the variance of the provided array. Make sure to replace data with your own array of numbers.

Example

Here is a complete example of how to use the variance calculation function:

```javascript const { calculateVariance } = require('./variance');

const sampleData = [5, 10, 15, 20, 25]; const result = calculateVariance(sampleData);

console.log(The variance of the sample data is: ${result}); ```

Variance Calculation

The variance is calculated using the formula:

[ Var(X) = \frac{1}{n} \sum{i=1}^{n} (Xi - \bar{X})^2 ]

Where: - ( Var(X) ) is the variance - ( n ) is the number of observations - ( X_i ) are the individual data points - ( \bar{X} ) is the mean of the data points

This implementation efficiently computes the mean and variance in a single traversal of the array, minimizing the time complexity.

API Reference

calculateVariance(data)

• Parameters:
  • data (Array): An array of numbers for which the variance is to be calculated.
• Returns:
  • number: The calculated variance of the input array.

Example Usage

javascript const variance = calculateVariance([1, 2, 3, 4, 5]); console.log(variance); // Output: 2.5

Performance

The algorithm runs in O(n) time complexity, making it suitable for large datasets. The one-pass nature ensures that you only loop through the data once, thus optimizing performance.

Testing

To ensure the reliability of the implementation, run the provided test suite. You can execute the tests using:

bash npm test

The test suite covers various scenarios, including edge cases and large datasets.

Contributing

We welcome contributions to enhance the functionality of this repository. If you have suggestions or improvements, please follow these steps:

1. Fork the repository.
2. Create a new branch for your feature or bug fix.
3. Make your changes and commit them.
4. Push your branch and submit a pull request.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Releases

To download the latest version of the project, visit the Releases section. Here you will find all the available versions for download.

Additional Resources

• JavaScript Array Methods
• Understanding Variance in Statistics
• Node.js Documentation

Contact

For any inquiries or support, feel free to open an issue in the repository or reach out directly through GitHub.

Acknowledgments

• Special thanks to the contributors and the community for their continuous support and feedback.
• This project is inspired by the need for efficient statistical calculations in JavaScript.

For further updates and releases, check out the Releases section.