Median Absolute Deviation

/**
 * Fintech Math Bootcamp · Lesson 044 of 120
 * Median Absolute Deviation
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Robust central spread without confusing two MADs
 * Rule:     raw MAD = median(|x − median(x)|)
 *
 * Try it:   Is 1.4826 a universal correction for every distribution?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson044() {
  const x = [1,2,2,4,9];
  const med = (a: number[]) => { const s=[...a].sort((p,q)=>p-q), m=Math.floor(s.length/2);
    return s.length % 2 ? s[m] : (s[m-1]+s[m])/2; };
  const center = med(x);
  const raw = med(x.map(v=>Math.abs(v-center)));
  const result = {raw, normalScaled: 1.4826*raw};
  return result;
}

export const checkedResult = {"raw":1,"normalScaled":1.4826};

// Run this file directly: npx tsx lessons/05-dispersion-shape-and-robust-statistics/044-median-absolute-deviation.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson044(), null, 2));
}

# Fintech Math Bootcamp · Lesson 044 of 120
# Median Absolute Deviation
# Module 05: Dispersion, Shape, and Robust Statistics
#
# Scenario: Robust central spread without confusing two MADs
# Rule:     raw MAD = median(|x − median(x)|)
#
# Try it:   Is 1.4826 a universal correction for every distribution?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json


def median(a: list) -> float:
    s = sorted(a)
    m = len(s) // 2
    return s[m] if len(s) % 2 else (s[m - 1] + s[m]) / 2


def lesson044() -> dict:
    x = [1, 2, 2, 4, 9]
    center = median(x)
    raw = median([abs(v - center) for v in x])
    return {"raw": raw, "normalScaled": 1.4826 * raw}


if __name__ == "__main__":
    print(json.dumps(lesson044(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 044 of 120
 * Median Absolute Deviation
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Robust central spread without confusing two MADs
 * Rule:     raw MAD = median(|x − median(x)|)
 *
 * Try it:   Is 1.4826 a universal correction for every distribution?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;

public class Main {
    static double median(double[] a) {
        double[] s = a.clone();
        Arrays.sort(s);
        int m = s.length / 2;
        return s.length % 2 == 1 ? s[m] : (s[m - 1] + s[m]) / 2;
    }

    static Map<String, Object> lesson044() {
        double[] x = {1, 2, 2, 4, 9};
        double center = median(x);
        double[] distances = new double[x.length];
        for (int i = 0; i < x.length; i++) distances[i] = Math.abs(x[i] - center);
        double raw = median(distances);
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("raw", raw);
        result.put("normalScaled", 1.4826 * raw);
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson044(), ""));
    }

    // --- Minimal JSON printer: maps keep insertion order, 2-space indent. ---

    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof String) return "\"" + value + "\"";
        if (value instanceof Double) return formatNumber((Double) value);
        if (value instanceof Number) return value.toString();
        if (value instanceof double[]) {
            List<Object> items = new ArrayList<Object>();
            for (double v : (double[]) value) items.add(v);
            return toJson(items, indent);
        }
        String inner = indent + "  ";
        StringBuilder sb = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            sb.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> entry : map.entrySet()) {
                sb.append(inner).append('"').append(entry.getKey()).append("\": ")
                  .append(toJson(entry.getValue(), inner))
                  .append(++i < map.size() ? ",\n" : "\n");
            }
            return sb.append(indent).append('}').toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        sb.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            sb.append(inner).append(toJson(list.get(i), inner))
              .append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return sb.append(indent).append(']').toString();
    }

    static String formatNumber(double v) {
        if (Double.isNaN(v) || Double.isInfinite(v)) return "null";
        if (v == Math.rint(v) && Math.abs(v) < 1e15) return Long.toString((long) v);
        return Double.toString(v);
    }
}

// Fintech Math Bootcamp · Lesson 044 of 120
// Median Absolute Deviation
// Module 05: Dispersion, Shape, and Robust Statistics
//
// Scenario: Robust central spread without confusing two MADs
// Rule:     raw MAD = median(|x − median(x)|)
//
// Try it:   Is 1.4826 a universal correction for every distribution?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
	"math"
	"slices"
)

// MAD holds the raw median absolute deviation and its normal-scaled version.
type MAD struct {
	Raw          float64 `json:"raw"`
	NormalScaled float64 `json:"normalScaled"`
}

func median(a []float64) float64 {
	s := slices.Clone(a)
	slices.Sort(s)
	m := len(s) / 2
	if len(s)%2 == 1 {
		return s[m]
	}
	return (s[m-1] + s[m]) / 2
}

func lesson044() MAD {
	x := []float64{1, 2, 2, 4, 9}
	center := median(x)
	distances := make([]float64, len(x))
	for i, v := range x {
		distances[i] = math.Abs(v - center)
	}
	raw := median(distances)
	return MAD{Raw: raw, NormalScaled: 1.4826 * raw}
}

func main() {
	out, _ := json.MarshalIndent(lesson044(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 044 of 120
 * Median Absolute Deviation
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Robust central spread without confusing two MADs
 * Rule:     raw MAD = median(|x − median(x)|)
 *
 * Try it:   Is 1.4826 a universal correction for every distribution?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

#include <algorithm>
#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

struct Json {
    enum class Kind { Null, Number, Text, Array, Object };
    Kind kind = Kind::Null;
    double number = 0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array elements or object values
};

Json num(double v) { Json j; j.kind = Json::Kind::Number; j.number = v; return j; }
Json str(const std::string& s) { Json j; j.kind = Json::Kind::Text; j.text = s; return j; }
Json arr(const std::vector<Json>& values) { Json j; j.kind = Json::Kind::Array; j.items = values; return j; }

Json arr(const std::vector<double>& values) {
    std::vector<Json> items;
    for (double v : values) items.push_back(num(v));
    return arr(items);
}

Json obj(const std::vector<std::pair<std::string, Json>>& fields) {
    Json j;
    j.kind = Json::Kind::Object;
    for (const auto& [key, value] : fields) { j.keys.push_back(key); j.items.push_back(value); }
    return j;
}

std::string formatNumber(double v) {
    if (!std::isfinite(v)) return "null";
    char buf[64];
    auto end = std::to_chars(buf, buf + sizeof buf, v).ptr;  // shortest round-trip form
    return std::string(buf, end);
}

void writeJson(std::ostream& out, const Json& j, const std::string& indent) {
    switch (j.kind) {
    case Json::Kind::Null: out << "null"; return;
    case Json::Kind::Number: out << formatNumber(j.number); return;
    case Json::Kind::Text: out << '"' << j.text << '"'; return;
    default: break;
    }
    bool isObject = j.kind == Json::Kind::Object;
    if (j.items.empty()) { out << (isObject ? "{}" : "[]"); return; }
    std::string inner = indent + "  ";
    out << (isObject ? "{\n" : "[\n");
    for (size_t i = 0; i < j.items.size(); ++i) {
        out << inner;
        if (isObject) out << '"' << j.keys[i] << "\": ";
        writeJson(out, j.items[i], inner);
        out << (i + 1 < j.items.size() ? ",\n" : "\n");
    }
    out << indent << (isObject ? '}' : ']');
}

// --- Lesson ---

double median(std::vector<double> s) {  // takes a copy, so sorting is local
    std::sort(s.begin(), s.end());
    size_t m = s.size() / 2;
    return s.size() % 2 ? s[m] : (s[m - 1] + s[m]) / 2;
}

Json lesson044() {
    const std::vector<double> x = {1, 2, 2, 4, 9};
    double center = median(x);
    std::vector<double> distances;
    for (double v : x) distances.push_back(std::abs(v - center));
    double raw = median(distances);
    return obj({{"raw", num(raw)}, {"normalScaled", num(1.4826 * raw)}});
}

int main() {
    writeJson(std::cout, lesson044(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 044 of 120
// Median Absolute Deviation
// Module 05: Dispersion, Shape, and Robust Statistics
//
// Scenario: Robust central spread without confusing two MADs
// Rule:     raw MAD = median(|x − median(x)|)
//
// Try it:   Is 1.4826 a universal correction for every distribution?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

#[allow(dead_code)]
enum Json {
    Null,
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

#[allow(dead_code)]
fn nums(values: &[f64]) -> Json {
    Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
}

#[allow(dead_code)]
fn obj(fields: Vec<(&str, Json)>) -> Json {
    Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
}

fn format_number(v: f64) -> String {
    if !v.is_finite() {
        return "null".to_string();
    }
    if v.fract() == 0.0 && v.abs() < 1e15 {
        return format!("{}", v as i64);
    }
    format!("{:?}", v) // shortest round-trip form
}

impl Json {
    fn render(&self, indent: &str) -> String {
        let inner = format!("{}  ", indent);
        match self {
            Json::Null => "null".to_string(),
            Json::Num(v) => format_number(*v),
            Json::Str(s) => format!("\"{}\"", s),
            Json::Arr(items) if items.is_empty() => "[]".to_string(),
            Json::Obj(fields) if fields.is_empty() => "{}".to_string(),
            Json::Arr(items) => {
                let lines: Vec<String> = items.iter().map(|v| format!("{}{}", inner, v.render(&inner))).collect();
                format!("[\n{}\n{}]", lines.join(",\n"), indent)
            }
            Json::Obj(fields) => {
                let lines: Vec<String> = fields
                    .iter()
                    .map(|(k, v)| format!("{}\"{}\": {}", inner, k, v.render(&inner)))
                    .collect();
                format!("{{\n{}\n{}}}", lines.join(",\n"), indent)
            }
        }
    }
}

// --- Lesson ---

fn median(a: &[f64]) -> f64 {
    let mut s = a.to_vec();
    s.sort_by(|p, q| p.partial_cmp(q).unwrap());
    let m = s.len() / 2;
    if s.len() % 2 == 1 { s[m] } else { (s[m - 1] + s[m]) / 2.0 }
}

fn lesson044() -> Json {
    let x: [f64; 5] = [1.0, 2.0, 2.0, 4.0, 9.0];
    let center = median(&x);
    let distances: Vec<f64> = x.iter().map(|&v| (v - center).abs()).collect();
    let raw = median(&distances);
    obj(vec![("raw", Json::Num(raw)), ("normalScaled", Json::Num(1.4826 * raw))])
}

fn main() {
    println!("{}", lesson044().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 044 of 120
 * Median Absolute Deviation
 * Module 05: Dispersion, Shape, and Robust Statistics
 *
 * Scenario: Robust central spread without confusing two MADs
 * Rule:     raw MAD = median(|x − median(x)|)
 *
 * Try it:   Is 1.4826 a universal correction for every distribution?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

using System;
using System.Linq;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson044(), options));

static double Median(double[] a)
{
    double[] s = a.OrderBy(v => v).ToArray();
    int m = s.Length / 2;
    return s.Length % 2 == 1 ? s[m] : (s[m - 1] + s[m]) / 2;
}

static object Lesson044()
{
    double[] x = { 1, 2, 2, 4, 9 };
    double center = Median(x);
    double raw = Median(x.Select(v => Math.Abs(v - center)).ToArray());
    return new { raw, normalScaled = 1.4826 * raw };
}