The Geometric Mean is a type of mean or average that indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). It is particularly useful for datasets that are related multiplicatively, such as rates of change, percentages, or ratios.
How to Calculate the Geometric Mean
To calculate the geometric mean of a set of n non-negative numbers (x1, x2, …, xn), you follow these steps:
Multiply all the numbers together: Product = x1 * x2 * ... * xn
Take the nth root of the product: Geometric Mean = (Product)1/n
Mathematically, this is represented as:
GM = (∏i=1n xi)1/n
Where:
GM is the Geometric Mean
xi represents each individual number in the dataset
n is the total count of numbers in the dataset
∏ denotes the product of the numbers
Why Use the Geometric Mean?
The geometric mean is more appropriate than the arithmetic mean in situations involving:
Averaging Rates of Change: For example, if an investment grows by 10% in year one and 20% in year two, the average annual growth rate is calculated using the geometric mean.
Calculating Average Investment Returns: When compounding returns over multiple periods, the geometric mean provides a more accurate picture of the average performance.
Averaging Ratios or Percentages: It's suitable for data that are inherently multiplicative.
Financial and Economic Analysis: Used in indices, inflation rates, and growth rates.
It's important to note that the geometric mean can only be calculated for non-negative numbers. If any number in the set is zero, the geometric mean will be zero. If there are negative numbers, the calculation becomes more complex and may not yield a real number.
Example Calculation
Let's calculate the geometric mean for the numbers 4, 8, and 32.
Multiply the numbers: 4 * 8 * 32 = 1024
Count the numbers: There are 3 numbers, so n = 3.
Take the 3rd root of the product:3√1024 = 10.079 (approximately)
So, the geometric mean of 4, 8, and 32 is approximately 10.079.
function calculateGeometricMean() {
var valuesInput = document.getElementById("values").value;
var resultsDiv = document.getElementById("geometricMeanResult");
if (!valuesInput) {
resultsDiv.innerText = "Please enter numbers.";
return;
}
var valuesArray = valuesInput.split(',')
.map(function(val) {
return val.trim();
})
.filter(function(val) {
return val !== ";
});
if (valuesArray.length === 0) {
resultsDiv.innerText = "No valid numbers entered.";
return;
}
var numbers = [];
var allPositive = true;
for (var i = 0; i < valuesArray.length; i++) {
var num = parseFloat(valuesArray[i]);
if (isNaN(num)) {
resultsDiv.innerText = "Invalid input. Please enter numbers only.";
return;
}
if (num < 0) {
allPositive = false;
}
numbers.push(num);
}
if (!allPositive) {
resultsDiv.innerText = "Geometric mean requires non-negative numbers.";
return;
}
if (numbers.includes(0)) {
resultsDiv.innerText = "0.000";
return;
}
var product = 1;
for (var i = 0; i < numbers.length; i++) {
product *= numbers[i];
}
var n = numbers.length;
var geometricMean = Math.pow(product, 1 / n);
resultsDiv.innerText = geometricMean.toFixed(3); // Display with 3 decimal places
}
function clearFields() {
document.getElementById("values").value = "";
document.getElementById("geometricMeanResult").innerText = "–";
}