Descriptive Statistics Calculator
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Descriptive Statistics Calculator
Your Statistics
Enter your data points above and click "Calculate Statistics" to see the results.
Understanding Descriptive Statistics
Descriptive statistics are fundamental tools in data analysis that help us summarize and understand the main features of a dataset. They provide a concise overview of the data's central tendency, dispersion, and shape, making it easier to interpret complex information.
Key Measures of Descriptive Statistics
- Mean (Average): The sum of all data points divided by the number of data points. It represents the central point of the data.
- Median: The middle value in a dataset that has been ordered from least to greatest. If there's an even number of data points, it's the average of the two middle values. It is less affected by outliers than the mean.
- Mode: The value that appears most frequently in the dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode.
- Range: The difference between the highest and lowest values in the dataset. It gives a simple measure of the data's spread.
- Variance: The average of the squared differences from the Mean. It measures how spread out the data is. A higher variance indicates that the data points are further from the mean.
- Standard Deviation: The square root of the Variance. It is a more interpretable measure of dispersion than variance because it is in the same units as the original data. It indicates the typical deviation of data points from the mean.
- Count: The total number of data points in the dataset.
How the Calculator Works
This calculator takes a list of numbers (your data points), separates them, and then applies the formulas for the descriptive statistics mentioned above. It handles potential errors, such as non-numeric input, and provides a clear output of the calculated statistics.
Formulas Used:
- Count (n): The number of valid numerical data points.
- Sum (Σx): The sum of all valid data points.
- Mean (x̄):
Σx / n
- Median: For ordered data
x_1, x_2, ..., x_n:
- If
n is odd: x_((n+1)/2)
- If
n is even: (x_(n/2) + x_(n/2 + 1)) / 2
- Mode: The value(s) with the highest frequency.
- Range:
Maximum Value - Minimum Value
- Variance (s²):
Σ(xᵢ - x̄)² / (n - 1) (for sample variance)
- Standard Deviation (s):
sqrt(Variance)
Use Cases
Descriptive statistics are invaluable in various fields:
- Business: Analyzing sales figures, customer demographics, or market research data.
- Science: Summarizing experimental results, survey data, or biological measurements.
- Finance: Understanding stock price movements, portfolio performance, or economic indicators.
- Education: Evaluating student test scores or performance metrics.
- Healthcare: Analyzing patient outcomes, disease prevalence, or treatment effectiveness.
function calculateStats() {
var dataInput = document.getElementById("dataInput").value;
var errorMessageElement = document.getElementById("errorMessage");
var calculationOutputElement = document.getElementById("calculationOutput");
// Clear previous results and error messages
calculationOutputElement.innerHTML = ";
errorMessageElement.textContent = ";
// Parse the input string into an array of numbers
var dataPoints = [];
if (dataInput) {
var rawValues = dataInput.split(',');
for (var i = 0; i < rawValues.length; i++) {
var trimmedValue = rawValues[i].trim();
if (trimmedValue !== '') {
var number = parseFloat(trimmedValue);
if (!isNaN(number)) {
dataPoints.push(number);
} else {
errorMessageElement.textContent = "Error: Please enter only valid numbers separated by commas.";
return;
}
}
}
}
if (dataPoints.length === 0) {
errorMessageElement.textContent = "Error: Please enter at least one data point.";
return;
}
// — Calculations —
var n = dataPoints.length;
var sum = 0;
for (var i = 0; i < n; i++) {
sum += dataPoints[i];
}
var mean = sum / n;
// Sort data for median and range calculations
var sortedData = dataPoints.slice().sort(function(a, b) { return a – b; });
var median;
if (n % 2 === 0) {
// Even number of data points
median = (sortedData[n / 2 – 1] + sortedData[n / 2]) / 2;
} else {
// Odd number of data points
median = sortedData[Math.floor(n / 2)];
}
var range = sortedData[n – 1] – sortedData[0];
// Calculate Variance and Standard Deviation
var sumSquaredDiffs = 0;
for (var i = 0; i < n; i++) {
sumSquaredDiffs += Math.pow(dataPoints[i] – mean, 2);
}
var variance = sumSquaredDiffs / (n – 1); // Sample variance
var standardDeviation = Math.sqrt(variance);
// Calculate Mode
var frequencyMap = {};
var maxFrequency = 0;
for (var i = 0; i maxFrequency) {
maxFrequency = frequencyMap[value];
}
}
var modes = [];
if (maxFrequency > 1) { // Only consider modes if a value appears more than once
for (var value in frequencyMap) {
if (frequencyMap[value] === maxFrequency) {
modes.push(parseFloat(value)); // Convert key back to number
}
}
}
var modeDisplay = modes.length > 0 ? modes.join(', ') : 'N/A (no repeating values)';
// — Display Results —
calculationOutputElement.innerHTML = `
Count
${n}
Sum
${sum.toFixed(4)}
Mean
${mean.toFixed(4)}
Median
${median.toFixed(4)}
Mode
${modeDisplay}
Range
${range.toFixed(4)}
Variance (Sample)
${variance.toFixed(4)}
Standard Deviation (Sample)
${standardDeviation.toFixed(4)}
`;
}