A weighted average is a type of average that assigns different levels of importance (weights) to different values in a dataset. Unlike a simple average where all values contribute equally, a weighted average allows certain values to have a greater influence on the final outcome. This is crucial in many real-world scenarios where not all data points are equally significant.
How to Calculate a Weighted Average
The formula for calculating a weighted average is as follows:
Weighted Average = Σ (value × weight) / Σ (weight)
Where:
value represents each individual data point.
weight represents the importance or significance assigned to each value.
Σ (Sigma) is the summation symbol, meaning "add up".
In simpler terms, you multiply each value by its corresponding weight, sum up all these products, and then divide that sum by the sum of all the weights.
When to Use a Weighted Average:
Calculating Grades: In academic settings, different assignments (like homework, quizzes, exams) often have different percentage values contributing to the final grade. For example, an exam might be worth 50% of the grade, while homework is only worth 10%.
Investment Portfolio Analysis: When assessing the performance of an investment portfolio, individual assets contribute differently based on the amount invested in each.
Statistical Data: In surveys or research, responses might be weighted based on demographic factors (like age, location, or income) to ensure the sample is representative of the population.
Cost Averaging: When calculating the average cost of an asset acquired at different price points over time.
Example Calculation:
Let's say you want to calculate your final grade in a course. You have two assignments:
Assignment 1: Value = 85, Weight = 0.4 (40%)
Assignment 2: Value = 72, Weight = 0.6 (60%)
Using the formula:
Multiply each value by its weight:
(85 × 0.4) = 34
(72 × 0.6) = 43.2
Sum the products: 34 + 43.2 = 77.2
Sum the weights: 0.4 + 0.6 = 1.0
Divide the sum of products by the sum of weights: 77.2 / 1.0 = 77.2
The weighted average grade for this course is 77.2.
function calculateWeightedAverage() {
var item1Value = parseFloat(document.getElementById("item1Value").value);
var item1Weight = parseFloat(document.getElementById("item1Weight").value);
var item2Value = parseFloat(document.getElementById("item2Value").value);
var item2Weight = parseFloat(document.getElementById("item2Weight").value);
var resultDiv = document.getElementById("result");
if (isNaN(item1Value) || isNaN(item1Weight) || isNaN(item2Value) || isNaN(item2Weight)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (item1Weight < 0 || item2Weight < 0) {
resultDiv.innerHTML = "Weights cannot be negative.";
return;
}
var sumOfProducts = (item1Value * item1Weight) + (item2Value * item2Weight);
var sumOfWeights = item1Weight + item2Weight;
if (sumOfWeights === 0) {
resultDiv.innerHTML = "The sum of weights cannot be zero.";
return;
}
var weightedAverage = sumOfProducts / sumOfWeights;
resultDiv.innerHTML = "Weighted Average: " + weightedAverage.toFixed(2) + "";
}