{
  "id": "mean-absolute-deviation",
  "version": "947f1c879a45",
  "status": "published",
  "name": "Mean Absolute Deviation Calculator",
  "question": "What is the mean absolute deviation?",
  "summary": "Computes the mean absolute deviation (MAD) of a list of numbers: the average distance of each number from the mean.",
  "category": "statistics",
  "subcategory": "descriptive",
  "url": "https://www.acalculator.org/statistics/mean-absolute-deviation-calculator",
  "markdown": "https://www.acalculator.org/statistics/mean-absolute-deviation-calculator.md",
  "kind": "function",
  "method": "MAD = Σ|x − mean| ÷ n, where mean = Σx ÷ n.",
  "assumptions": [
    "The deviations are measured from the mean, not the median.",
    "The sum of distances is divided by n, the count of numbers."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "input": {
        "title": "Your numbers",
        "description": "The numbers, separated by commas, spaces, semicolons, or new lines.",
        "type": "array",
        "items": {
          "type": "number"
        }
      }
    }
  },
  "outputs": {
    "mad": {
      "label": "Mean absolute deviation",
      "description": "The average of the distances |x − mean| of each number from the mean.",
      "format": "number"
    },
    "mean": {
      "label": "Mean",
      "description": "The sum divided by the count.",
      "format": "number"
    },
    "count": {
      "label": "Count",
      "description": "How many numbers are in the list.",
      "format": "integer"
    },
    "sum": {
      "label": "Sum",
      "description": "All the numbers added up.",
      "format": "number"
    },
    "min": {
      "label": "Smallest",
      "description": "The smallest number in the list.",
      "format": "number"
    },
    "max": {
      "label": "Largest",
      "description": "The largest number in the list.",
      "format": "number"
    },
    "range": {
      "label": "Range",
      "description": "The largest number minus the smallest.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "input": "1, 2, 3, 4, 5, 6, 7, 8, 9, 10"
    },
    "outputs": {
      "mad": 2.5,
      "mean": 5.5,
      "count": 10,
      "sum": 55,
      "min": 1,
      "max": 10,
      "range": 9
    },
    "text": "The mean absolute deviation of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 2.5, around a mean of 5.5."
  },
  "examples": [
    {
      "given": {
        "input": [
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10
        ]
      },
      "expect": {
        "mad": 2.5,
        "mean": 5.5,
        "range": 9
      },
      "source": "hand calculation in content.mdx: distances 4.5, 3.5, 2.5, 1.5, 0.5 twice each sum to 25; 25 ÷ 10 = 2.5; NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (variance, standard deviation, average absolute deviation). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm"
    },
    {
      "given": {
        "input": [
          2,
          4,
          4,
          4,
          5,
          5,
          7,
          9
        ]
      },
      "expect": {
        "mad": 1.5,
        "mean": 5
      },
      "source": "hand calculation in content.mdx: distances 3, 1, 1, 1, 0, 0, 2, 4 sum to 12; 12 ÷ 8 = 1.5; NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (variance, standard deviation, average absolute deviation). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm"
    },
    {
      "given": {
        "input": [
          1.5,
          2.5,
          3.5,
          10.25
        ]
      },
      "expect": {
        "mad": 2.90625,
        "mean": 4.4375
      },
      "source": "hand calculation in content.mdx: distances 2.9375, 1.9375, 0.9375, 5.8125 sum to 11.625; 11.625 ÷ 4 = 2.90625; NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (variance, standard deviation, average absolute deviation). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm"
    },
    {
      "given": {
        "input": [
          100
        ]
      },
      "expect": {
        "mad": 0,
        "mean": 100
      },
      "source": "hand calculation in content.mdx: one number is its own mean, at distance 0; NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (variance, standard deviation, average absolute deviation). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm"
    }
  ],
  "sources": [
    "NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (variance, standard deviation, average absolute deviation). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}