Enter your data into the table below. The calculator will automatically compute the median and related values.
Class Interval
Frequency (f)
Cumulative Frequency (cf)
Midpoint (x)
fx
Median Calculation Results
—
Median Class
—
N (Total Frequency)
—
L (Lower Boundary)
—
CF (Cumulative Freq. before Median Class)
—
f (Frequency of Median Class)
—
h (Class Width)
—
Formula Used: Median = L + [ (N/2 – CF) / f ] * h
What is Calculating Median from a Frequency Table?
Calculating the median from a frequency table is a fundamental statistical technique used to find the middle value in a dataset that has been organized into groups or classes. Unlike a simple list of numbers where you just find the middle one, a frequency table summarizes data by showing how often each value or range of values occurs. This method is crucial when dealing with large datasets or continuous data that is best represented in intervals.
Who should use it? This method is invaluable for statisticians, data analysts, researchers, students, and anyone working with grouped data. It's particularly useful in fields like education (analyzing test scores), economics (understanding income distribution), manufacturing (quality control), and social sciences (demographic studies). If you have data presented in bins or ranges, understanding how to find the median from its frequency table is essential for grasping the central tendency of your data.
Common Misconceptions: A frequent misunderstanding is that the median from a frequency table is simply the midpoint of the class that contains the N/2 cumulative frequency. While this class is identified as the 'median class', the actual median calculation involves a more precise interpolation within that class using the formula. Another misconception is confusing the median with the mean (average) or mode (most frequent value), which are different measures of central tendency and calculated differently from frequency tables.
Median from Frequency Table Formula and Mathematical Explanation
The process of calculating the median from a frequency table involves several steps to pinpoint the exact middle value, even when the exact data points aren't listed individually. The core idea is to identify the 'median class' – the interval where the median value lies – and then interpolate within that class.
Step-by-Step Derivation:
Calculate Total Frequency (N): Sum all the frequencies (f) in the table. This gives you the total number of data points.
Find N/2: Divide the total frequency (N) by 2. This value represents the position of the median observation.
Determine Cumulative Frequencies (cf): Calculate the cumulative frequency for each class. This is done by adding the frequency of the current class to the cumulative frequency of the previous class. The cumulative frequency of the first class is just its own frequency.
Identify the Median Class: Find the first class interval where the cumulative frequency (cf) is greater than or equal to N/2. This interval is known as the median class.
Identify Key Values:
L (Lower Boundary of the Median Class): This is the lower limit of the median class interval. For continuous data, it's often the actual lower limit. For discrete data or grouped intervals, it might be adjusted (e.g., for 10-20, the lower boundary might be 9.5 if the data is integers). Our calculator uses the lower limit as provided.
N: The total frequency calculated in step 1.
CF (Cumulative Frequency of the Class Preceding the Median Class): This is the cumulative frequency of the class *just before* the identified median class.
f (Frequency of the Median Class): This is the frequency of the median class itself.
h (Class Width): The width of the median class interval (Upper Limit – Lower Limit). Ensure consistency across classes for accurate results.
Apply the Median Formula: Use the following formula to calculate the median:
Median = L + [ (N/2 – CF) / f ] * h
This formula essentially calculates how far into the median class the N/2 observation falls and adds that proportion to the lower boundary of the class.
Variables Table
Variable
Meaning
Unit
Typical Range
L
Lower boundary of the median class
Data Unit
Depends on data range
N
Total frequency (sum of all frequencies)
Count
≥ 1
CF
Cumulative frequency of the class preceding the median class
Count
0 to N
f
Frequency of the median class
Count
≥ 1
h
Width of the median class interval
Data Unit
Positive value
Median
The calculated median value
Data Unit
Within the range of the data
Practical Examples (Real-World Use Cases)
Example 1: Student Test Scores
A teacher wants to find the median score for a class of 50 students based on their test results grouped into intervals.
Frequency Table:
Score Interval
Frequency (f)
50-59
5
60-69
10
70-79
15
80-89
12
90-99
8
Calculation Steps:
N = 5 + 10 + 15 + 12 + 8 = 50
N/2 = 50 / 2 = 25
Cumulative Frequencies:
50-59: cf = 5
60-69: cf = 5 + 10 = 15
70-79: cf = 15 + 15 = 30
80-89: cf = 30 + 12 = 42
90-99: cf = 42 + 8 = 50
Median Class: The first class with cf ≥ 25 is 70-79 (cf=30).
Values:
L = 70 (Lower limit of the median class)
N = 50
CF = 15 (Cumulative frequency before the median class)
f = 15 (Frequency of the median class)
h = 10 (Class width: 79 – 70 + 1, or assuming intervals are 70 to 79.99… width is 10)
Interpretation: The median test score is approximately 76.67. This means that 50% of the students scored below 76.67, and 50% scored above it. This gives a better sense of the central performance than the average, as it's less affected by extremely high or low scores.
Example 2: Daily Website Visitors
An analyst tracks daily website visitors over a month and groups the data.
Frequency Table:
Visitors per Day
Frequency (f)
100-199
7
200-299
10
300-399
8
400-499
5
Calculation Steps:
N = 7 + 10 + 8 + 5 = 30
N/2 = 30 / 2 = 15
Cumulative Frequencies:
100-199: cf = 7
200-299: cf = 7 + 10 = 17
300-399: cf = 17 + 8 = 25
400-499: cf = 25 + 5 = 30
Median Class: The first class with cf ≥ 15 is 200-299 (cf=17).
Values:
L = 200 (Lower limit of the median class)
N = 30
CF = 7 (Cumulative frequency before the median class)
f = 10 (Frequency of the median class)
h = 100 (Class width: 299 – 200 + 1, or assuming intervals are 200 to 299.99… width is 100)
Interpretation: The median number of daily website visitors is 280. This indicates that on half the days, the website received 280 or fewer visitors, and on the other half, it received 280 or more. This is a robust measure of typical daily traffic.
How to Use This Frequency Table Median Calculator
Our interactive calculator simplifies the process of finding the median from a frequency table. Follow these simple steps:
Input Data:
Start by defining your class intervals and their corresponding frequencies. You can add or remove rows using the "Add Row" and "Remove Last Row" buttons to match your dataset.
For each row, enter the lower and upper bounds of the class interval (e.g., "50-59" or just the lower bound if intervals are uniform and width is implied) and the frequency (the count of data points within that interval).
Ensure your class intervals are contiguous and cover the entire range of your data.
Calculate: Once your data is entered, click the "Calculate Median" button.
Review Results: The calculator will display:
Primary Result (Median): The calculated median value for your dataset.
Intermediate Values: Key figures used in the calculation, including the Median Class, Total Frequency (N), Lower Boundary (L), Cumulative Frequency before Median Class (CF), Frequency of Median Class (f), and Class Width (h).
Formula Used: A clear explanation of the formula applied.
Interpret: Use the median value to understand the central point of your grouped data. It represents the value below which 50% of the observations fall.
Reset or Copy: Use the "Reset" button to clear the fields and start over. Use the "Copy Results" button to copy all calculated values and assumptions for use elsewhere.
Decision-Making Guidance: The median is particularly useful when your data might be skewed or contain outliers. For instance, in income data, the median income is often more representative of the typical person than the average (mean) income, which can be inflated by a few very high earners. Use the median to get a robust measure of central tendency.
Key Factors That Affect Median from Frequency Table Results
While the median calculation itself is formulaic, several underlying data characteristics and choices in setting up the frequency table can influence the final result and its interpretation:
Class Interval Width (h): A narrower class width provides a more precise estimate of the median, as the interpolation within the median class is based on a smaller range. Wider intervals can smooth out variations but might reduce accuracy. Consistency in class width is crucial for reliable calculations.
Number of Classes: Using too few classes can oversimplify the data distribution, potentially masking important features and leading to a less accurate median. Conversely, too many classes (especially with low frequencies in each) can make the table sparse and harder to interpret.
Data Distribution Skewness: If the data is heavily skewed (e.g., a long tail of high values), the median will be closer to the bulk of the data than the mean. Understanding the skewness helps in choosing the appropriate measure of central tendency. The median is robust to outliers, meaning extreme values have little impact on it.
Accuracy of Frequencies: The entire calculation hinges on the accuracy of the frequency counts for each class. Errors in counting or recording data will directly lead to an incorrect median.
Definition of Class Boundaries (L): The choice of the lower boundary (L) for the median class is critical. If dealing with continuous data, using true class boundaries (e.g., 9.5 for a 10-19 class) provides more accuracy than simply using the lower limit (10). Our calculator uses the provided lower limit, assuming it's appropriate for the data context.
Data Type and Grouping Method: Whether the data is discrete or continuous affects how intervals are defined and boundaries are set. The method used to group the data initially (e.g., equal intervals, unequal intervals) directly impacts the structure of the frequency table and subsequent median calculation.
Completeness of Data (N): The total frequency (N) must accurately reflect all observations. Missing data points can skew the N/2 position and thus the median calculation.
Frequently Asked Questions (FAQ)
Q1: What is the difference between median and mean from a frequency table?
A1: The mean (average) is calculated by summing the product of each class midpoint and its frequency (Σfx) and dividing by the total frequency (N). The median is the middle value, found by interpolation within the median class. The mean is sensitive to outliers, while the median is not.
Q2: Can I calculate the median if the class intervals are unequal?
A2: Yes, you can. The formula remains the same: Median = L + [ (N/2 – CF) / f ] * h. However, ensure 'h' is the width of the *median class* specifically. Unequal widths can sometimes make interpretation trickier, but the calculation is valid.
Q3: What if N/2 falls exactly on a cumulative frequency boundary?
A3: If N/2 equals the cumulative frequency (CF) of a class, the median is the upper boundary of that class. If N/2 falls exactly between two cumulative frequencies, you still use the formula; the median will be calculated within the next class interval.
Q4: How do I handle open-ended intervals (e.g., "Below 50" or "100 and above")?
A4: Open-ended intervals make precise median calculation difficult without assumptions. For "Below 50", you need to assume a lower boundary (often 0). For "100 and above", you need to assume a class width based on previous intervals or estimate an upper boundary. This often requires additional context or assumptions.
Q5: Does the calculator handle discrete data (e.g., number of children)?
A5: Yes, the calculator works for discrete data. When entering class intervals for discrete data (e.g., 0-4, 5-9), ensure 'L' is the true lower boundary (e.g., 4.5 for the 5-9 class if data is integers) and 'h' is the correct width (e.g., 5). If you input 5 as L and 10 as h for the 5-9 class, the calculation assumes intervals like [5, 15).
Q6: What does the median class represent?
A6: The median class is the class interval that contains the median value. It's identified as the first class where the cumulative frequency is greater than or equal to half the total frequency (N/2).
Q7: Why is the median sometimes preferred over the mean?
A7: The median is preferred when the data distribution is skewed or contains extreme outliers, as it provides a more typical or representative central value. For example, median house prices or median incomes are often reported because a few very expensive properties or high earners can significantly inflate the mean.
Q8: Can I use this method for calculating quartiles or percentiles?
A8: Yes, the underlying principle is the same. Quartiles (Q1, Q3) and percentiles divide the data into four or one hundred parts, respectively. You identify the relevant position (N/4, 3N/4 for quartiles; N/100 * P for percentiles) and find the corresponding class and apply a similar interpolation formula.
Easily calculate cumulative frequencies for your datasets.
var tableBody = document.getElementById("tableBody");
var resultsContainer = document.getElementById("resultsContainer");
var mainResult = document.getElementById("mainResult");
var medianClassSpan = document.getElementById("medianClass");
var totalFrequencySpan = document.getElementById("totalFrequency");
var lowerBoundarySpan = document.getElementById("lowerBoundary");
var cumulativeFreqBeforeSpan = document.getElementById("cumulativeFreqBefore");
var medianClassFrequencySpan = document.getElementById("medianClassFrequency");
var classWidthSpan = document.getElementById("classWidth");
var chartInstance = null; // To hold the chart object
var ctx = document.getElementById('frequencyChart').getContext('2d');
// Initialize with a few rows
function initializeTable() {
for (var i = 0; i < 3; i++) {
addRow();
}
updateChart(); // Initial chart update
}
function addRow() {
var rowCount = tableBody.rows.length;
var newRow = tableBody.insertRow(rowCount);
var intervalCell = newRow.insertCell(0);
var frequencyCell = newRow.insertCell(1);
var cumulativeFreqCell = newRow.insertCell(2);
var midpointCell = newRow.insertCell(3);
var fxCell = newRow.insertCell(4);
intervalCell.innerHTML = '';
frequencyCell.innerHTML = ";
cumulativeFreqCell.innerHTML = ";
midpointCell.innerHTML = ";
fxCell.innerHTML = ";
// Add event listeners for interval input to potentially update calculations
intervalCell.querySelector('input').addEventListener('input', updateCalculations);
}
function removeRow() {
var rowCount = tableBody.rows.length;
if (rowCount > 1) {
tableBody.deleteRow(rowCount – 1);
updateCalculations();
}
}
function updateCalculations() {
var rows = tableBody.rows;
var cumulativeFrequency = 0;
var totalFrequency = 0;
var fxSum = 0;
var medianClassFound = false;
var medianClassDetails = { L: null, CF: null, f: null, h: null, medianClassIndex: -1 };
// First pass: Calculate cumulative frequencies, midpoints, fx, and total frequency
for (var i = 0; i < rows.length; i++) {
var row = rows[i];
var intervalInput = row.cells[0].querySelector('input');
var frequencyInput = row.cells[1].querySelector('input');
var cumulativeFreqInput = row.cells[2].querySelector('input');
var midpointInput = row.cells[3].querySelector('input');
var fxInput = row.cells[4].querySelector('input');
var frequency = parseFloat(frequencyInput.value);
var intervalValue = intervalInput.value;
// Validate frequency
if (isNaN(frequency) || frequency 0) {
for (var i = 0; i = nOver2 && !medianClassFound) {
medianClassFound = true;
var L = 0;
var h = 0;
var CF_prev = (i > 0) ? parseFloat(rows[i-1].cells[2].querySelector('input').value) : 0;
// Extract L and h from interval
var parts = intervalValue.split('-');
if (parts.length === 2) {
var lower = parseFloat(parts[0]);
var upper = parseFloat(parts[1]);
if (!isNaN(lower) && !isNaN(upper)) {
L = lower; // Using lower limit as L
h = upper – lower + 1; // Assuming inclusive integer ranges, e.g., 10-19 has width 10
// If data is continuous or intervals are like [10, 20), h = upper – lower
}
}
medianClassDetails = {
L: L,
CF: CF_prev,
f: currentFrequency,
h: h,
medianClassIndex: i
};
// Calculate median using the formula
if (currentFrequency > 0) {
median = L + ((nOver2 – CF_prev) / currentFrequency) * h;
} else {
median = L; // Edge case: frequency is 0
}
break; // Found the median class, exit loop
}
}
}
// Display results
totalFrequencySpan.textContent = totalFrequency.toFixed(0);
if (median !== null && !isNaN(median)) {
mainResult.textContent = median.toFixed(2);
resultsContainer.style.display = 'block';
if (medianClassFound) {
medianClassSpan.textContent = rows[medianClassDetails.medianClassIndex].cells[0].querySelector('input').value;
lowerBoundarySpan.textContent = medianClassDetails.L.toFixed(2);
cumulativeFreqBeforeSpan.textContent = medianClassDetails.CF.toFixed(0);
medianClassFrequencySpan.textContent = medianClassDetails.f.toFixed(0);
classWidthSpan.textContent = medianClassDetails.h.toFixed(0);
} else {
medianClassSpan.textContent = 'N/A';
lowerBoundarySpan.textContent = '–';
cumulativeFreqBeforeSpan.textContent = '–';
medianClassFrequencySpan.textContent = '–';
classWidthSpan.textContent = '–';
}
} else {
mainResult.textContent = '–';
resultsContainer.style.display = 'none';
}
updateChart(); // Update chart after calculations
}
function calculateMedian() {
updateCalculations();
}
function resetCalculator() {
tableBody.innerHTML = "; // Clear existing rows
initializeTable(); // Add default rows
resultsContainer.style.display = 'none';
mainResult.textContent = '–';
medianClassSpan.textContent = '–';
totalFrequencySpan.textContent = '–';
lowerBoundarySpan.textContent = '–';
cumulativeFreqBeforeSpan.textContent = '–';
medianClassFrequencySpan.textContent = '–';
classWidthSpan.textContent = '–';
if (chartInstance) {
chartInstance.destroy();
chartInstance = null;
}
// Re-initialize chart canvas if it was removed or needs reset
var chartCanvas = document.getElementById('frequencyChart');
if (!chartCanvas) {
chartCanvas = document.createElement('canvas');
chartCanvas.id = 'frequencyChart';
document.getElementById('frequencyTableContainer').appendChild(chartCanvas);
}
updateChart(); // Ensure chart is drawn after reset
}
function copyResults() {
var resultText = "Median Calculation Results:\n";
resultText += "—————————–\n";
resultText += "Median: " + mainResult.textContent + "\n";
resultText += "Median Class: " + medianClassSpan.textContent + "\n";
resultText += "Total Frequency (N): " + totalFrequencySpan.textContent + "\n";
resultText += "Lower Boundary (L): " + lowerBoundarySpan.textContent + "\n";
resultText += "Cumulative Frequency before Median Class (CF): " + cumulativeFreqBeforeSpan.textContent + "\n";
resultText += "Frequency of Median Class (f): " + medianClassFrequencySpan.textContent + "\n";
resultText += "Class Width (h): " + classWidthSpan.textContent + "\n";
resultText += "\nFormula: Median = L + [ (N/2 – CF) / f ] * h\n";
// Add table data
resultText += "\nFrequency Table Data:\n";
resultText += "Interval\tFrequency\tCumulative Frequency\tMidpoint\tfx\n";
var rows = tableBody.rows;
for (var i = 0; i < rows.length; i++) {
var cells = rows[i].cells;
resultText += cells[0].querySelector('input').value + "\t";
resultText += cells[1].querySelector('input').value + "\t";
resultText += cells[2].querySelector('input').value + "\t";
resultText += cells[3].querySelector('input').value + "\t";
resultText += cells[4].querySelector('input').value + "\n";
}
// Use a temporary textarea to copy
var textArea = document.createElement("textarea");
textArea.value = resultText;
document.body.appendChild(textArea);
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'Results copied!' : 'Copy failed';
console.log(msg);
// Optionally show a temporary message to the user
var tempMessage = document.createElement('div');
tempMessage.textContent = msg;
tempMessage.style.position = 'fixed';
tempMessage.style.bottom = '10px';
tempMessage.style.left = '50%';
tempMessage.style.transform = 'translateX(-50%)';
tempMessage.style.backgroundColor = '#004a99';
tempMessage.style.color = 'white';
tempMessage.style.padding = '10px';
tempMessage.style.borderRadius = '5px';
document.body.appendChild(tempMessage);
setTimeout(function() {
document.body.removeChild(tempMessage);
}, 2000);
} catch (err) {
console.log('Oops, unable to copy');
}
document.body.removeChild(textArea);
}
// Charting Logic (using pure Canvas API)
function updateChart() {
var rows = tableBody.rows;
var labels = [];
var frequencies = [];
var cumulativeFrequencies = [];
var totalFreq = 0;
var currentCF = 0;
for (var i = 0; i < rows.length; i++) {
var intervalInput = rows[i].cells[0].querySelector('input');
var frequencyInput = rows[i].cells[1].querySelector('input');
var cfInput = rows[i].cells[2].querySelector('input');
var intervalLabel = intervalInput.value || `Row ${i+1}`;
var frequency = parseFloat(frequencyInput.value) || 0;
labels.push(intervalLabel);
frequencies.push(frequency);
currentCF += frequency;
cumulativeFrequencies.push(currentCF);
totalFreq = currentCF;
}
var chartCanvas = document.getElementById('frequencyChart');
if (!chartCanvas) {
// Create canvas if it doesn't exist
chartCanvas = document.createElement('canvas');
chartCanvas.id = 'frequencyChart';
document.getElementById('frequencyTableContainer').insertBefore(chartCanvas, document.querySelector('.button-group'));
}
var ctx = chartCanvas.getContext('2d');
// Destroy previous chart instance if it exists
if (window.chartInstance) {
window.chartInstance.destroy();
}
// Create new chart
window.chartInstance = new Chart(ctx, {
type: 'bar', // Use bar chart for frequencies
data: {
labels: labels,
datasets: [{
label: 'Frequency (f)',
data: frequencies,
backgroundColor: 'rgba(0, 74, 153, 0.6)', // Primary color
borderColor: 'rgba(0, 74, 153, 1)',
borderWidth: 1,
yAxisID: 'y-axis-freq' // Assign to frequency y-axis
},
{
label: 'Cumulative Frequency (cf)',
data: cumulativeFrequencies,
type: 'line', // Use line for cumulative frequency
borderColor: 'rgba(40, 167, 69, 1)', // Success color
backgroundColor: 'rgba(40, 167, 69, 0.2)',
borderWidth: 2,
fill: false,
tension: 0.1,
yAxisID: 'y-axis-cf' // Assign to cumulative frequency y-axis
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
x: {
title: {
display: true,
text: 'Class Interval'
}
},
'y-axis-freq': { // Frequency axis
type: 'linear',
position: 'left',
title: {
display: true,
text: 'Frequency'
},
beginAtZero: true,
grid: {
color: 'rgba(200, 200, 200, 0.2)'
}
},
'y-axis-cf': { // Cumulative Frequency axis
type: 'linear',
position: 'right',
title: {
display: true,
text: 'Cumulative Frequency'
},
beginAtZero: true,
grid: {
drawOnChartArea: false, // Only want grid lines for the primary y-axis
}
}
},
plugins: {
title: {
display: true,
text: 'Frequency Distribution and Cumulative Frequency'
},
legend: {
display: true,
position: 'top'
}
}
}
});
}
// Initial setup
document.addEventListener('DOMContentLoaded', function() {
initializeTable();
// Add a canvas element for the chart
var chartCanvas = document.createElement('canvas');
chartCanvas.id = 'frequencyChart';
document.getElementById('frequencyTableContainer').insertBefore(chartCanvas, document.querySelector('.button-group'));
updateChart(); // Draw initial chart
});
// Helper function to parse interval and calculate width
function getIntervalDetails(intervalString) {
var lower = NaN, upper = NaN, width = NaN;
if (intervalString) {
var parts = intervalString.split(/[-–—]/); // Handle different dashes
if (parts.length === 2) {
lower = parseFloat(parts[0].trim());
upper = parseFloat(parts[1].trim());
if (!isNaN(lower) && !isNaN(upper)) {
// Assuming integer data, e.g., 10-19 means 10, 11, …, 19 (10 values)
// If data is continuous or intervals are [10, 20), width is upper – lower
width = upper – lower + 1;
}
}
}
return { lower: lower, upper: upper, width: width };
}
// Override updateCalculations to use getIntervalDetails for L and h
function updateCalculations() {
var rows = tableBody.rows;
var cumulativeFrequency = 0;
var totalFrequency = 0;
var fxSum = 0;
var medianClassFound = false;
var medianClassDetails = { L: null, CF: null, f: null, h: null, medianClassIndex: -1 };
// First pass: Calculate cumulative frequencies, midpoints, fx, and total frequency
for (var i = 0; i < rows.length; i++) {
var row = rows[i];
var intervalInput = row.cells[0].querySelector('input');
var frequencyInput = row.cells[1].querySelector('input');
var cumulativeFreqInput = row.cells[2].querySelector('input');
var midpointInput = row.cells[3].querySelector('input');
var fxInput = row.cells[4].querySelector('input');
var frequency = parseFloat(frequencyInput.value);
var intervalValue = intervalInput.value;
if (isNaN(frequency) || frequency 0) {
for (var i = 0; i = nOver2 && !medianClassFound) {
medianClassFound = true;
var L = intervalDetails.lower;
var h = intervalDetails.width;
var CF_prev = (i > 0) ? parseFloat(rows[i-1].cells[2].querySelector('input').value) : 0;
medianClassDetails = {
L: L,
CF: CF_prev,
f: currentFrequency,
h: h,
medianClassIndex: i
};
if (currentFrequency > 0 && !isNaN(L) && !isNaN(h)) {
median = L + ((nOver2 – CF_prev) / currentFrequency) * h;
} else if (!isNaN(L)) {
median = L; // Handle cases where f=0 or interval is invalid
} else {
median = NaN; // Cannot calculate
}
break;
}
}
}
// Display results
totalFrequencySpan.textContent = totalFrequency.toFixed(0);
if (median !== null && !isNaN(median)) {
mainResult.textContent = median.toFixed(2);
resultsContainer.style.display = 'block';
if (medianClassFound) {
medianClassSpan.textContent = rows[medianClassDetails.medianClassIndex].cells[0].querySelector('input').value;
lowerBoundarySpan.textContent = !isNaN(medianClassDetails.L) ? medianClassDetails.L.toFixed(2) : '–';
cumulativeFreqBeforeSpan.textContent = !isNaN(medianClassDetails.CF) ? medianClassDetails.CF.toFixed(0) : '–';
medianClassFrequencySpan.textContent = !isNaN(medianClassDetails.f) ? medianClassDetails.f.toFixed(0) : '–';
classWidthSpan.textContent = !isNaN(medianClassDetails.h) ? medianClassDetails.h.toFixed(0) : '–';
} else {
medianClassSpan.textContent = 'N/A';
lowerBoundarySpan.textContent = '–';
cumulativeFreqBeforeSpan.textContent = '–';
medianClassFrequencySpan.textContent = '–';
classWidthSpan.textContent = '–';
}
} else {
mainResult.textContent = '–';
resultsContainer.style.display = 'none';
}
updateChart();
}
// Ensure Chart.js is loaded or use native canvas drawing
// For this example, we'll assume Chart.js is available or implement native drawing.
// Since the prompt requires NO external libraries, we'll use native canvas drawing.
// The updateChart function above uses Chart.js syntax. Let's replace it with native canvas.
// — Native Canvas Drawing Implementation —
function drawNativeChart(labels, frequencies, cumulativeFrequencies, totalFreq) {
var chartCanvas = document.getElementById('frequencyChart');
if (!chartCanvas) {
chartCanvas = document.createElement('canvas');
chartCanvas.id = 'frequencyChart';
document.getElementById('frequencyTableContainer').insertBefore(chartCanvas, document.querySelector('.button-group'));
}
var ctx = chartCanvas.getContext('2d');
ctx.clearRect(0, 0, chartCanvas.width, chartCanvas.height); // Clear previous drawing
var chartWidth = chartCanvas.clientWidth;
var chartHeight = 300; // Fixed height for simplicity, or make responsive
chartCanvas.width = chartWidth;
chartCanvas.height = chartHeight;
if (!labels || labels.length === 0) return;
var padding = 40;
var chartAreaWidth = chartWidth – 2 * padding;
var chartAreaHeight = chartHeight – 2 * padding;
// Find max values for scaling
var maxFreq = Math.max(…frequencies, 0);
var maxCF = Math.max(…cumulativeFrequencies, 0);
var maxY = Math.max(maxFreq, maxCF);
if (maxY === 0) maxY = 1; // Avoid division by zero
// Scale factors
var xStep = chartAreaWidth / labels.length;
var yFreqScale = chartAreaHeight / maxFreq;
var yCfScale = chartAreaHeight / maxCF;
// Draw Axes
ctx.strokeStyle = '#ccc';
ctx.lineWidth = 1;
ctx.font = '12px Arial';
ctx.fillStyle = '#333';
// Y-axis (Frequency)
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, chartHeight – padding);
ctx.stroke();
ctx.textAlign = 'right';
ctx.fillText(maxFreq.toFixed(0), padding – 5, padding);
ctx.fillText('0', padding – 5, chartHeight – padding);
ctx.save();
ctx.translate(padding – 10, chartHeight / 2);
ctx.rotate(-90 * Math.PI / 180);
ctx.fillText('Frequency', 0, 0);
ctx.restore();
// Y-axis (Cumulative Frequency) – secondary axis simulation
ctx.beginPath();
ctx.moveTo(chartWidth – padding, padding);
ctx.lineTo(chartWidth – padding, chartHeight – padding);
ctx.stroke();
ctx.textAlign = 'left';
ctx.fillText(maxCF.toFixed(0), chartWidth – padding + 5, padding);
ctx.fillText('0', chartWidth – padding + 5, chartHeight – padding);
ctx.save();
ctx.translate(chartWidth – 15, chartHeight / 2);
ctx.rotate(90 * Math.PI / 180);
ctx.fillText('Cumulative Frequency', 0, 0);
ctx.restore();
// X-axis
ctx.beginPath();
ctx.moveTo(padding, chartHeight – padding);
ctx.lineTo(chartWidth – padding, chartHeight – padding);
ctx.stroke();
ctx.textAlign = 'center';
for (var i = 0; i < labels.length; i++) {
ctx.fillText(labels[i], padding + xStep * (i + 0.5), chartHeight – padding + 15);
}
// Draw Bars (Frequency)
ctx.fillStyle = 'rgba(0, 74, 153, 0.6)';
ctx.strokeStyle = 'rgba(0, 74, 153, 1)';
ctx.lineWidth = 1;
var barWidth = xStep * 0.8;
var barOffset = xStep * 0.1;
for (var i = 0; i < frequencies.length; i++) {
var barHeight = frequencies[i] * yFreqScale;
var x = padding + xStep * i + barOffset;
var y = chartHeight – padding – barHeight;
ctx.fillRect(x, y, barWidth, barHeight);
ctx.strokeRect(x, y, barWidth, barHeight);
}
// Draw Line (Cumulative Frequency)
ctx.strokeStyle = 'rgba(40, 167, 69, 1)';
ctx.lineWidth = 2;
ctx.fillStyle = 'rgba(40, 167, 69, 0.2)';
ctx.beginPath();
ctx.moveTo(padding + xStep * 0.5, chartHeight – padding – cumulativeFrequencies[0] * yCfScale); // Start at midpoint of first bar
for (var i = 1; i < cumulativeFrequencies.length; i++) {
ctx.lineTo(padding + xStep * (i + 0.5), chartHeight – padding – cumulativeFrequencies[i] * yCfScale);
}
ctx.stroke();
// Add fill below the line (optional)
ctx.lineTo(padding + xStep * (cumulativeFrequencies.length – 0.5), chartHeight – padding); // Go to bottom right of last bar
ctx.lineTo(padding + xStep * 0.5, chartHeight – padding); // Go to bottom left of first bar
ctx.closePath();
ctx.fill();
// Add Legend
var legendHtml = '
';
legendHtml += ' Frequency (f)';
legendHtml += ' Cumulative Frequency (cf)';
legendHtml += '
';
var existingLegend = chartCanvas.nextElementSibling;
if (existingLegend && existingLegend.classList.contains('chart-legend')) {
existingLegend.outerHTML = legendHtml; // Update existing legend
} else {
chartCanvas.insertAdjacentHTML('afterend', legendHtml);
}
}
// Replace the Chart.js updateChart with native drawing call
function updateChart() {
var rows = tableBody.rows;
var labels = [];
var frequencies = [];
var cumulativeFrequencies = [];
var currentCF = 0;
for (var i = 0; i < rows.length; i++) {
var intervalInput = rows[i].cells[0].querySelector('input');
var frequencyInput = rows[i].cells[1].querySelector('input');
var cfInput = rows[i].cells[2].querySelector('input');
var intervalLabel = intervalInput.value || `Row ${i+1}`;
var frequency = parseFloat(frequencyInput.value) || 0;
labels.push(intervalLabel);
frequencies.push(frequency);
currentCF += frequency;
cumulativeFrequencies.push(currentCF);
}
drawNativeChart(labels, frequencies, cumulativeFrequencies);
}
// Initial call to set up the table and chart on page load
document.addEventListener('DOMContentLoaded', function() {
initializeTable();
// Ensure canvas element exists before calling updateChart
var chartCanvas = document.getElementById('frequencyChart');
if (!chartCanvas) {
chartCanvas = document.createElement('canvas');
chartCanvas.id = 'frequencyChart';
document.getElementById('frequencyTableContainer').insertBefore(chartCanvas, document.querySelector('.button-group'));
}
updateChart();
});