function calculateStatistics() {
var numbersString = document.getElementById("numbersInput").value;
var numbers = numbersString.split(',').map(function(item) {
return parseFloat(item.trim());
}).filter(function(num) {
return !isNaN(num);
});
if (numbers.length === 0) {
document.getElementById("meanResult").textContent = "N/A";
document.getElementById("medianResult").textContent = "N/A";
document.getElementById("modeResult").textContent = "N/A";
document.getElementById("rangeResult").textContent = "N/A";
alert("Please enter valid numbers separated by commas.");
return;
}
// Sort numbers for Median and Range
var sortedNumbers = numbers.slice().sort(function(a, b) {
return a – b;
});
// Calculate Mean
var sum = numbers.reduce(function(acc, curr) {
return acc + curr;
}, 0);
var mean = sum / numbers.length;
document.getElementById("meanResult").textContent = mean.toFixed(2);
// Calculate Median
var median;
var mid = Math.floor(sortedNumbers.length / 2);
if (sortedNumbers.length % 2 === 0) {
median = (sortedNumbers[mid – 1] + sortedNumbers[mid]) / 2;
} else {
median = sortedNumbers[mid];
}
document.getElementById("medianResult").textContent = median.toFixed(2);
// Calculate Mode
var counts = {};
numbers.forEach(function(num) {
counts[num] = (counts[num] || 0) + 1;
});
var maxCount = 0;
for (var num in counts) {
if (counts[num] > maxCount) {
maxCount = counts[num];
}
}
var modes = [];
for (var num in counts) {
if (counts[num] === maxCount) {
modes.push(parseFloat(num));
}
}
// Check if all numbers appear only once (no distinct mode)
if (maxCount === 1 && numbers.length > 1) {
document.getElementById("modeResult").textContent = "No distinct mode (all numbers appear once)";
} else if (numbers.length === 1) {
document.getElementById("modeResult").textContent = numbers[0];
}
else {
document.getElementById("modeResult").textContent = modes.join(', ');
}
// Calculate Range
var range = sortedNumbers[sortedNumbers.length – 1] – sortedNumbers[0];
document.getElementById("rangeResult").textContent = range.toFixed(2);
}
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
max-width: 600px;
margin: 30px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
.calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
font-size: 1.8em;
}
.calculator-form .form-group {
margin-bottom: 18px;
}
.calculator-form label {
display: block;
margin-bottom: 8px;
color: #555;
font-weight: bold;
font-size: 1.05em;
}
.calculator-form input[type="text"] {
width: calc(100% – 22px);
padding: 12px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
box-sizing: border-box;
transition: border-color 0.3s ease;
}
.calculator-form input[type="text"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 5px rgba(0, 123, 255, 0.3);
}
.calculate-button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
margin-top: 20px;
}
.calculate-button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.calculate-button:active {
transform: translateY(0);
}
.calculator-results {
background-color: #e9f7ff;
border: 1px solid #b3e0ff;
border-radius: 8px;
padding: 20px;
margin-top: 25px;
}
.calculator-results h3 {
color: #0056b3;
margin-top: 0;
margin-bottom: 15px;
font-size: 1.5em;
text-align: center;
}
.calculator-results p {
font-size: 1.1em;
color: #333;
margin-bottom: 10px;
line-height: 1.6;
}
.calculator-results p strong {
color: #007bff;
min-width: 80px; /* Align labels */
display: inline-block;
}
.calculator-results span {
font-weight: normal;
color: #222;
}
Understanding Mean, Median, Mode, and Range
In statistics, mean, median, mode, and range are fundamental concepts used to describe and summarize a set of data. They provide different insights into the central tendency and spread of numerical values, making them invaluable tools for analysis in various fields, from finance to science.
What is the Mean?
The mean, often referred to as the average, is calculated by summing all the numbers in a dataset and then dividing by the count of those numbers. It represents the typical value in a dataset. The mean is sensitive to outliers (extremely high or low values), which can significantly skew its value.
Formula: Mean = (Sum of all numbers) / (Total count of numbers)
Example: For the numbers 10, 20, 30, 40, 50:
- Sum = 10 + 20 + 30 + 40 + 50 = 150
- Count = 5
- Mean = 150 / 5 = 30
What is the Median?
The median is the middle value in a dataset when the numbers are arranged in ascending or descending order. Unlike the mean, the median is not affected by outliers, making it a more robust measure of central tendency for skewed distributions.
How to calculate:
- Arrange the numbers in order from smallest to largest.
- If there is an odd number of values, the median is the middle number.
- If there is an even number of values, the median is the average of the two middle numbers.
Example (Odd count): For the numbers 10, 20, 30, 40, 50:
- Ordered: 10, 20, 30, 40, 50
- Median = 30
Example (Even count): For the numbers 10, 20, 30, 40, 50, 60:
- Ordered: 10, 20, 30, 40, 50, 60
- Median = (30 + 40) / 2 = 35
What is the Mode?
The mode is the number that appears most frequently in a dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode at all if all numbers appear with the same frequency.
How to find: Count the occurrences of each number and identify the one(s) with the highest frequency.
Example (Single Mode): For the numbers 10, 20, 20, 30, 40:
- 10 appears once
- 20 appears twice
- 30 appears once
- 40 appears once
- Mode = 20
Example (Multiple Modes): For the numbers 10, 10, 20, 30, 30, 40:
- 10 appears twice
- 20 appears once
- 30 appears twice
- 40 appears once
- Modes = 10, 30
Example (No Distinct Mode): For the numbers 10, 20, 30, 40, 50:
- Each number appears once.
- No distinct mode.
What is the Range?
The range is the difference between the highest and lowest values in a dataset. It provides a simple measure of the spread or variability of the data.
Formula: Range = (Highest number) – (Lowest number)
Example: For the numbers 10, 20, 30, 40, 50:
- Highest number = 50
- Lowest number = 10
- Range = 50 – 10 = 40
Why are these measures important?
Each of these statistical measures offers a unique perspective on a dataset:
- Mean: Gives a general idea of the average value, useful for symmetrical distributions.
- Median: Provides the true middle point, especially useful for skewed data (e.g., income distribution).
- Mode: Identifies the most common value, useful for categorical data or finding popular items.
- Range: Shows the overall spread of the data, indicating variability.
By using these measures together, you can gain a comprehensive understanding of your data's characteristics, helping you make more informed decisions and draw accurate conclusions.