Percentiles, Quantiles, and Quartiles

/**
 * Fintech Math Bootcamp · Lesson 036 of 120
 * Percentiles, Quantiles, and Quartiles
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A percentile is incomplete without its interpolation rule
 * Rule:     type 7: h=(n−1)p, interpolate adjacent values
 *
 * Try it:   Was five hours observed in the sample?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson036() {
  const x = [1, 2, 2, 4, 9].sort((a,b) => a-b);
  const q = (p: number) => { // type-7 linear interpolation
    const h = (x.length-1)*p, i = Math.floor(h);
    return x[i] + (h-i)*(x[Math.min(i+1,x.length-1)]-x[i]);
  };
  const result = {q25:q(.25), q50:q(.5), q75:q(.75), q80:q(.8)};
  return result;
}

export const checkedResult = {"q25":2,"q50":2,"q75":4,"q80":5.000000000000001};

// Run this file directly: npx tsx lessons/04-location-ranking-and-exploratory-summaries/036-percentiles-quantiles-and-quartiles.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson036(), null, 2));
}

# Fintech Math Bootcamp · Lesson 036 of 120
# Percentiles, Quantiles, and Quartiles
# Module 04: Location, Ranking, and Exploratory Summaries
#
# Scenario: A percentile is incomplete without its interpolation rule
# Rule:     type 7: h=(n−1)p, interpolate adjacent values
#
# Try it:   Was five hours observed in the sample?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json
import math


def lesson036() -> dict:
    x = sorted([1, 2, 2, 4, 9])

    def q(p: float) -> float:  # type-7 linear interpolation
        h = (len(x) - 1) * p
        i = math.floor(h)
        return x[i] + (h - i) * (x[min(i + 1, len(x) - 1)] - x[i])

    return {"q25": q(0.25), "q50": q(0.5), "q75": q(0.75), "q80": q(0.8)}


if __name__ == "__main__":
    print(json.dumps(lesson036(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 036 of 120
 * Percentiles, Quantiles, and Quartiles
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A percentile is incomplete without its interpolation rule
 * Rule:     type 7: h=(n−1)p, interpolate adjacent values
 *
 * Try it:   Was five hours observed in the sample?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
 * 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 {
    // Type-7 linear interpolation between adjacent order statistics; x must be sorted.
    static double quantile7(double[] x, double p) {
        double h = (x.length - 1) * p;
        int i = (int) Math.floor(h);
        return x[i] + (h - i) * (x[Math.min(i + 1, x.length - 1)] - x[i]);
    }

    static Map<String, Object> lesson036() {
        double[] x = {1, 2, 2, 4, 9};
        Arrays.sort(x);
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("q25", quantile7(x, 0.25));
        result.put("q50", quantile7(x, 0.5));
        result.put("q75", quantile7(x, 0.75));
        result.put("q80", quantile7(x, 0.8));
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson036(), ""));
    }

    // --- 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 036 of 120
// Percentiles, Quantiles, and Quartiles
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: A percentile is incomplete without its interpolation rule
// Rule:     type 7: h=(n−1)p, interpolate adjacent values
//
// Try it:   Was five hours observed in the sample?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

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

// Quantiles holds type-7 quantiles at four probabilities.
type Quantiles struct {
	Q25 float64 `json:"q25"`
	Q50 float64 `json:"q50"`
	Q75 float64 `json:"q75"`
	Q80 float64 `json:"q80"`
}

// quantile7 interpolates linearly between adjacent order statistics (type 7).
func quantile7(x []float64, p float64) float64 {
	h := float64(len(x)-1) * p
	i := int(math.Floor(h))
	return x[i] + (h-float64(i))*(x[min(i+1, len(x)-1)]-x[i])
}

func lesson036() Quantiles {
	x := []float64{1, 2, 2, 4, 9}
	sort.Float64s(x)
	return Quantiles{
		Q25: quantile7(x, 0.25),
		Q50: quantile7(x, 0.5),
		Q75: quantile7(x, 0.75),
		Q80: quantile7(x, 0.8),
	}
}

func main() {
	out, _ := json.MarshalIndent(lesson036(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 036 of 120
 * Percentiles, Quantiles, and Quartiles
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A percentile is incomplete without its interpolation rule
 * Rule:     type 7: h=(n−1)p, interpolate adjacent values
 *
 * Try it:   Was five hours observed in the sample?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
 * 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 ---

// Type-7 linear interpolation between adjacent order statistics; x must be sorted.
double quantile7(const std::vector<double>& x, double p) {
    double h = (x.size() - 1) * p;
    size_t i = static_cast<size_t>(std::floor(h));
    return x[i] + (h - i) * (x[std::min(i + 1, x.size() - 1)] - x[i]);
}

Json lesson036() {
    std::vector<double> x = {1, 2, 2, 4, 9};
    std::sort(x.begin(), x.end());
    return obj({
        {"q25", num(quantile7(x, 0.25))},
        {"q50", num(quantile7(x, 0.5))},
        {"q75", num(quantile7(x, 0.75))},
        {"q80", num(quantile7(x, 0.8))},
    });
}

int main() {
    writeJson(std::cout, lesson036(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 036 of 120
// Percentiles, Quantiles, and Quartiles
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: A percentile is incomplete without its interpolation rule
// Rule:     type 7: h=(n−1)p, interpolate adjacent values
//
// Try it:   Was five hours observed in the sample?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
// 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 ---

/// Type-7 linear interpolation between adjacent order statistics; `x` must be sorted.
fn quantile7(x: &[f64], p: f64) -> f64 {
    let h = (x.len() - 1) as f64 * p;
    let i = h.floor() as usize;
    x[i] + (h - i as f64) * (x[(i + 1).min(x.len() - 1)] - x[i])
}

fn lesson036() -> Json {
    let mut x: Vec<f64> = vec![1.0, 2.0, 2.0, 4.0, 9.0];
    x.sort_by(|a, b| a.partial_cmp(b).unwrap());
    obj(vec![
        ("q25", Json::Num(quantile7(&x, 0.25))),
        ("q50", Json::Num(quantile7(&x, 0.5))),
        ("q75", Json::Num(quantile7(&x, 0.75))),
        ("q80", Json::Num(quantile7(&x, 0.8))),
    ])
}

fn main() {
    println!("{}", lesson036().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 036 of 120
 * Percentiles, Quantiles, and Quartiles
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: A percentile is incomplete without its interpolation rule
 * Rule:     type 7: h=(n−1)p, interpolate adjacent values
 *
 * Try it:   Was five hours observed in the sample?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/percentiles-quantiles-and-quartiles/
 * 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(Lesson036(), options));

static object Lesson036()
{
    double[] x = new double[] { 1, 2, 2, 4, 9 }.OrderBy(v => v).ToArray();

    // Type-7 linear interpolation between adjacent order statistics.
    double Q(double p)
    {
        double h = (x.Length - 1) * p;
        int i = (int)Math.Floor(h);
        return x[i] + (h - i) * (x[Math.Min(i + 1, x.Length - 1)] - x[i]);
    }

    return new { q25 = Q(0.25), q50 = Q(0.5), q75 = Q(0.75), q80 = Q(0.8) };
}