Frequency Distribution Calculator

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Frequency Distribution Calculator

This calculator helps you organize a set of raw data into a frequency distribution table. A frequency distribution is a summary of how often different values or ranges of values appear in a dataset. It's a fundamental tool in statistics for understanding the patterns and spread of data.

(Leave blank or 0 for calculator to suggest based on Sturges' formula)

Understanding Frequency Distributions

A frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval. This method helps in summarizing large datasets, making them easier to understand and interpret.

Key Components:

  • Raw Data: The original, unorganized data points collected.
  • Classes (Bins): Intervals or categories into which the raw data is grouped. The number of classes can be chosen by the user or determined by statistical formulas like Sturges' rule.
  • Class Width: The size of each class interval. It's typically calculated as (Range / Number of Classes).
  • Class Boundaries: The lower and upper limits of each class. These define which data points fall into a specific class.
  • Frequency: The number of data points that fall within a specific class interval.
  • Relative Frequency: The proportion of data points that fall within a specific class. It's calculated as (Frequency / Total Number of Data Points) and often expressed as a percentage.
  • Cumulative Frequency: The sum of frequencies for a given class and all preceding classes. It shows how many data points are less than or equal to the upper boundary of that class.
  • Cumulative Relative Frequency: The sum of relative frequencies for a given class and all preceding classes, usually expressed as a percentage.

How to Use the Calculator:

  1. Enter Raw Data: Input your numerical data points into the "Raw Data" text area, separated by commas.
  2. Set Number of Classes: You can specify the desired number of classes. If you leave it blank or enter 0, the calculator will suggest an optimal number of classes using Sturges' formula (k = 1 + 3.322 * log10(n), where n is the number of data points).
  3. Calculate: Click the "Calculate Distribution" button.
  4. Review Results: The calculator will display a table showing the class intervals, their frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies. It will also provide summary statistics like the minimum, maximum, range, and total number of data points.

Example:

Let's say you have the following test scores for a class: 65, 70, 72, 75, 78, 80, 81, 83, 85, 88, 90, 92, 95, 98, 100

If you input this data and choose 5 classes, the calculator might produce a distribution similar to this:

Class Interval Frequency Relative Frequency (%) Cumulative Frequency Cumulative Relative Frequency (%)
[65.0 – 71.0) 2 13.33% 2 13.33%
[71.0 – 77.0) 3 20.00% 5 33.33%
[77.0 – 83.0) 4 26.67% 9 60.00%
[83.0 – 89.0) 2 13.33% 11 73.33%
[89.0 – 95.0) 3 20.00% 14 93.33%
[95.0 – 101.0] 1 6.67% 15 100.00%

This table quickly shows that most students scored between 77 and 83, and 60% of students scored 83 or below.

function calculateFrequencyDistribution() { var rawDataInput = document.getElementById("rawData").value; var numClassesInput = document.getElementById("numClasses").value; var resultDiv = document.getElementById("result"); var data = rawDataInput.split(',').map(function(item) { return parseFloat(item.trim()); }).filter(function(item) { return !isNaN(item); }); if (data.length === 0) { resultDiv.innerHTML = 'Please enter valid numerical data.'; return; } data.sort(function(a, b) { return a – b; }); var minVal = data[0]; var maxVal = data[data.length – 1]; var range = maxVal – minVal; var n = data.length; var numClasses; if (numClassesInput && parseInt(numClassesInput) > 0) { numClasses = parseInt(numClassesInput); } else { // Sturges' formula for suggested number of classes numClasses = Math.round(1 + 3.322 * Math.log10(n)); if (numClasses n) numClasses = n; // Cannot have more classes than data points } if (numClasses === 0) numClasses = 1; // Fallback if Sturges' formula results in 0 for very small n var classWidth = range / numClasses; // Adjust class width slightly if range is 0 (all data points are the same) if (range === 0) { classWidth = 1; // A single class of width 1 minVal = data[0] – 0.5; // Center the single value maxVal = data[0] + 0.5; range = 1; } else { // Ensure class width is slightly larger to cover maxVal if it falls exactly on an upper boundary // This helps with floating point precision and ensures maxVal is included in the last bin var calculatedMax = minVal + numClasses * classWidth; if (calculatedMax < maxVal) { classWidth = (maxVal – minVal) / numClasses; // Recalculate to ensure coverage // Add a tiny epsilon to classWidth to ensure maxVal is strictly less than the upper bound of the next (non-existent) class classWidth += 1e-9; } } var classes = []; var frequencies = new Array(numClasses).fill(0); var cumulativeFrequencies = []; var relativeFrequencies = []; var cumulativeRelativeFrequencies = []; // Determine class boundaries for (var i = 0; i < numClasses; i++) { var lowerBound = minVal + i * classWidth; var upperBound = minVal + (i + 1) * classWidth; classes.push({ lower: lowerBound, upper: upperBound }); } // Tally frequencies for (var j = 0; j < n; j++) { var value = data[j]; for (var k = 0; k < numClasses; k++) { var lower = classes[k].lower; var upper = classes[k].upper; // For all but the last class, use [lower, upper) // For the last class, use [lower, upper] to ensure maxVal is included if (k = lower && value = lower && value <= upper) { frequencies[k]++; break; } } } } // Calculate relative, cumulative frequencies var currentCumulativeFreq = 0; for (var i = 0; i < numClasses; i++) { currentCumulativeFreq += frequencies[i]; cumulativeFrequencies.push(currentCumulativeFreq); relativeFrequencies.push((frequencies[i] / n) * 100); cumulativeRelativeFrequencies.push((currentCumulativeFreq / n) * 100); } var output = '

Frequency Distribution Results

'; output += 'Total Data Points: ' + n + "; output += 'Minimum Value: ' + minVal.toFixed(2) + "; output += 'Maximum Value: ' + maxVal.toFixed(2) + "; output += 'Range: ' + range.toFixed(2) + "; output += 'Number of Classes Used: ' + numClasses + "; output += 'Calculated Class Width: ' + classWidth.toFixed(2) + "; output += ''; output += ''; output += ''; output += ''; output += ''; output += ''; output += ''; output += ''; for (var i = 0; i < numClasses; i++) { var lowerBoundFormatted = classes[i].lower.toFixed(2); var upperBoundFormatted = classes[i].upper.toFixed(2); var intervalString = '[' + lowerBoundFormatted + ' – ' + upperBoundFormatted + (i < numClasses – 1 ? ')' : ']'); output += ''; output += ''; output += ''; output += ''; output += ''; output += ''; output += ''; } output += '
Class IntervalFrequencyRelative Frequency (%)Cumulative FrequencyCumulative Relative Frequency (%)
' + intervalString + '' + frequencies[i] + '' + relativeFrequencies[i].toFixed(2) + '%' + cumulativeFrequencies[i] + '' + cumulativeRelativeFrequencies[i].toFixed(2) + '%
'; resultDiv.innerHTML = output; }

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