{
    "name": "Weighted Average Calculator",
    "url": "https://calculators.geekmidst.com/calculators/weighted-average-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/weighted-average-calculator.md",
    "category": "Statistics & probability",
    "description": "Find the weighted mean of a list of values with their weights, plus the sum of weights, the unweighted mean for comparison and the weighted standard deviation.",
    "summary": "A weighted average lets some values count more than others: multiply each value by its weight, add them up and divide by the total weight.",
    "also_called": [
        "Weighted mean calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "values",
            "label": "Values",
            "type": "textarea",
            "default": "80, 90, 70"
        },
        {
            "name": "weights",
            "label": "Weights, same order",
            "type": "textarea",
            "default": "20, 30, 50"
        }
    ],
    "outputs": [
        {
            "key": "weighted_mean",
            "label": "Weighted average",
            "format": "number"
        },
        {
            "key": "sum_weights",
            "label": "Sum of weights",
            "format": "number"
        },
        {
            "key": "sum_products",
            "label": "Sum of value × weight",
            "format": "number"
        },
        {
            "key": "simple_mean",
            "label": "Unweighted mean, for comparison",
            "format": "number"
        },
        {
            "key": "weighted_sd",
            "label": "Weighted standard deviation (population form)",
            "format": "number"
        },
        {
            "key": "n",
            "label": "Number of values",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "x̄_w = Σwᵢxᵢ ÷ Σwᵢ;  weighted SD = √(Σwᵢ(xᵢ − x̄_w)² ÷ Σwᵢ)",
        "variables": {
            "xᵢ": "value i",
            "wᵢ": "weight of value i (non-negative)"
        }
    },
    "worked_example": {
        "inputs": {
            "values": "80, 90, 70",
            "weights": "20, 30, 50"
        },
        "steps": [
            "Products: 80 × 20 = 1600, 90 × 30 = 2700, 70 × 50 = 3500; total 7800.",
            "Total weight = 20 + 30 + 50 = 100.",
            "Weighted average = 7800 ÷ 100 = 78, versus a simple mean of 80."
        ],
        "result": "Marks of 80, 90 and 70 weighted 20%, 30% and 50% average 78, lower than the simple mean because the lowest mark carries half the weight."
    },
    "interpretation": "The weighted average is pulled toward the values with the most weight. If it differs a lot from the simple mean, the heavily weighted items are unusual. The weighted SD uses the population (frequency-weight) form, dividing by the total weight.",
    "assumptions": [
        "Weights are relative importance or frequencies; only their proportions matter."
    ],
    "limitations": [
        "For averaging rates or ratios (speeds, prices per unit), make sure the weights are the right denominator, such as time or quantity, or the result will be misleading."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Do the weights need to add up to 100 or 1?",
            "answer": "No. The calculation divides by the total weight, so 2, 3, 5 gives the same answer as 20%, 30%, 50%."
        },
        {
            "question": "How do I average percentages from groups of different sizes?",
            "answer": "Use each group’s size as its weight; that gives the overall percentage for all groups combined."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Average Calculator",
            "url": "https://calculators.geekmidst.com/calculators/average-calculator"
        },
        {
            "name": "Weighted GPA Calculator",
            "url": "https://calculators.geekmidst.com/calculators/weighted-gpa-calculator"
        },
        {
            "name": "Weighted Assignment Score Calculator",
            "url": "https://calculators.geekmidst.com/calculators/weighted-assignment-score-calculator"
        },
        {
            "name": "Statistics Calculator",
            "url": "https://calculators.geekmidst.com/calculators/statistics-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}