Sturges’ Formula Calculator

Understanding Sturges' Rule

Formula for Sturges' Rule

The formula for calculating the number of bins (\(k\)) is:

Key Concepts

• Data Visualization: Using an appropriate number of bins ensures your histogram effectively represents the underlying data distribution without over-smoothing or overfitting.
• Sample Size Dependency: The number of bins increases with the sample size, reflecting finer granularity in larger datasets.
• Ceiling Function: Ensures the number of bins is always an integer, as fractional bins are not possible in practice.

Real-Life Applications

Sturges' Rule is widely applied in various fields to enhance data visualization:

• Finance: Creating histograms to analyze the distribution of stock returns or risk metrics.
• Healthcare: Visualizing patient data distributions, such as age or test scores.
• Education: Analyzing grade distributions or survey results.

Limitations of Sturges' Rule

• Normality Assumption: The rule is less effective for non-normal data distributions, where more advanced binning methods may be required.
• Large Sample Sizes: For very large datasets, the bins suggested by Sturges' Rule may oversimplify the distribution.
• Data Granularity: The rule may not work well for highly granular or categorical data, where bins need to reflect specific intervals or categories.

Python Implementation

import math

def sturges_rule(n):
    """
    Calculate the optimal number of bins using Sturges' Rule.

    Parameters:
        n (int): Sample size

    Returns:
        int: Number of bins
    """
    if n <= 0:
        raise ValueError("Sample size must be greater than 0.")

    return math.ceil(math.log2(n) + 1)

# Example usage
sample_size = 100
bins = sturges_rule(sample_size)
print(f"Optimal number of bins: {bins}")

sturges_rule <- function(n) {
    # Check if the sample size is valid
    if (n <= 0) {
        stop("Sample size must be greater than 0.")
    }

    # Calculate the number of bins
    bins <- ceiling(log2(n) + 1)
    return(bins)
}

# Example usage
sample_size <- 100
bins <- sturges_rule(sample_size)
cat(sprintf("Optimal number of bins: %d\n", bins))

/**
 * Calculate the optimal number of bins using Sturges' Rule.
 * @param {number} n - Sample size
 * @returns {number} - Number of bins
 */
function sturgesRule(n) {
    if (n <= 0 || isNaN(n)) {
        throw new Error("Sample size must be greater than 0.");
    }

    // Calculate the number of bins
    return Math.ceil(Math.log2(n) + 1);
}

// Example usage
const sampleSize = 100;
const bins = sturgesRule(sampleSize);
console.log(`Optimal number of bins: ${bins}`);

Further Reading