Ranks, Ties, and Percentile Rank

/**
 * Fintech Math Bootcamp · Lesson 037 of 120
 * Ranks, Ties, and Percentile Rank
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: Tied scores need a fair, explicit rank convention
 * Rule:     average ties; percentile rank = 100(r−1)/(n−1)
 *
 * Try it:   Do the tied twos receive ranks two and three under average ties?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson037() {
  const x = [1,2,2,4,9];
  const ranks = x.map(v => {
    const below = x.filter(y => y<v).length;
    const equal = x.filter(y => y===v).length;
    return below + (equal+1)/2;
  });
  const result = {ranks, percentileRanks:ranks.map(r=>100*(r-1)/(x.length-1))};
  return result;
}

export const checkedResult = {"ranks":[1,2.5,2.5,4,5],"percentileRanks":[0,37.5,37.5,75,100]};

// Run this file directly: npx tsx lessons/04-location-ranking-and-exploratory-summaries/037-ranks-ties-and-percentile-rank.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson037(), null, 2));
}

# Fintech Math Bootcamp · Lesson 037 of 120
# Ranks, Ties, and Percentile Rank
# Module 04: Location, Ranking, and Exploratory Summaries
#
# Scenario: Tied scores need a fair, explicit rank convention
# Rule:     average ties; percentile rank = 100(r−1)/(n−1)
#
# Try it:   Do the tied twos receive ranks two and three under average ties?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json


def lesson037() -> dict:
    x = [1, 2, 2, 4, 9]

    def average_rank(v: float) -> float:
        below = sum(1 for y in x if y < v)
        equal = sum(1 for y in x if y == v)
        return below + (equal + 1) / 2

    ranks = [average_rank(v) for v in x]
    percentile_ranks = [100 * (r - 1) / (len(x) - 1) for r in ranks]
    return {"ranks": ranks, "percentileRanks": percentile_ranks}


if __name__ == "__main__":
    print(json.dumps(lesson037(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 037 of 120
 * Ranks, Ties, and Percentile Rank
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: Tied scores need a fair, explicit rank convention
 * Rule:     average ties; percentile rank = 100(r−1)/(n−1)
 *
 * Try it:   Do the tied twos receive ranks two and three under average ties?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

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

public class Main {
    static Map<String, Object> lesson037() {
        double[] x = {1, 2, 2, 4, 9};
        double[] ranks = new double[x.length];
        double[] percentileRanks = new double[x.length];
        for (int i = 0; i < x.length; i++) {
            int below = 0, equal = 0;
            for (double y : x) {
                if (y < x[i]) below++;
                else if (y == x[i]) equal++;
            }
            ranks[i] = below + (equal + 1) / 2.0;
            percentileRanks[i] = 100 * (ranks[i] - 1) / (x.length - 1);
        }
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("ranks", ranks);
        result.put("percentileRanks", percentileRanks);
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson037(), ""));
    }

    // --- 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 037 of 120
// Ranks, Ties, and Percentile Rank
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: Tied scores need a fair, explicit rank convention
// Rule:     average ties; percentile rank = 100(r−1)/(n−1)
//
// Try it:   Do the tied twos receive ranks two and three under average ties?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
)

// Ranking holds average-tie ranks and the matching percentile ranks.
type Ranking struct {
	Ranks           []float64 `json:"ranks"`
	PercentileRanks []float64 `json:"percentileRanks"`
}

func lesson037() Ranking {
	x := []float64{1, 2, 2, 4, 9}
	n := float64(len(x))
	ranks := make([]float64, len(x))
	percentileRanks := make([]float64, len(x))
	for i, v := range x {
		below, equal := 0.0, 0.0
		for _, y := range x {
			if y < v {
				below++
			} else if y == v {
				equal++
			}
		}
		ranks[i] = below + (equal+1)/2
		percentileRanks[i] = 100 * (ranks[i] - 1) / (n - 1)
	}
	return Ranking{Ranks: ranks, PercentileRanks: percentileRanks}
}

func main() {
	out, _ := json.MarshalIndent(lesson037(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 037 of 120
 * Ranks, Ties, and Percentile Rank
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: Tied scores need a fair, explicit rank convention
 * Rule:     average ties; percentile rank = 100(r−1)/(n−1)
 *
 * Try it:   Do the tied twos receive ranks two and three under average ties?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
 * 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 ---

Json lesson037() {
    const std::vector<double> x = {1, 2, 2, 4, 9};
    std::vector<double> ranks, percentileRanks;
    for (double v : x) {
        auto below = std::count_if(x.begin(), x.end(), [v](double y) { return y < v; });
        auto equal = std::count_if(x.begin(), x.end(), [v](double y) { return y == v; });
        double rank = below + (equal + 1) / 2.0;
        ranks.push_back(rank);
        percentileRanks.push_back(100 * (rank - 1) / (x.size() - 1));
    }
    return obj({{"ranks", arr(ranks)}, {"percentileRanks", arr(percentileRanks)}});
}

int main() {
    writeJson(std::cout, lesson037(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 037 of 120
// Ranks, Ties, and Percentile Rank
// Module 04: Location, Ranking, and Exploratory Summaries
//
// Scenario: Tied scores need a fair, explicit rank convention
// Rule:     average ties; percentile rank = 100(r−1)/(n−1)
//
// Try it:   Do the tied twos receive ranks two and three under average ties?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
// 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 lesson037() -> Json {
    let x: [f64; 5] = [1.0, 2.0, 2.0, 4.0, 9.0];
    let ranks: Vec<f64> = x
        .iter()
        .map(|&v| {
            let below = x.iter().filter(|&&y| y < v).count() as f64;
            let equal = x.iter().filter(|&&y| y == v).count() as f64;
            below + (equal + 1.0) / 2.0
        })
        .collect();
    let n = x.len() as f64;
    let percentile_ranks: Vec<f64> = ranks.iter().map(|&r| 100.0 * (r - 1.0) / (n - 1.0)).collect();
    obj(vec![("ranks", nums(&ranks)), ("percentileRanks", nums(&percentile_ranks))])
}

fn main() {
    println!("{}", lesson037().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 037 of 120
 * Ranks, Ties, and Percentile Rank
 * Module 04: Location, Ranking, and Exploratory Summaries
 *
 * Scenario: Tied scores need a fair, explicit rank convention
 * Rule:     average ties; percentile rank = 100(r−1)/(n−1)
 *
 * Try it:   Do the tied twos receive ranks two and three under average ties?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/location-ranking-and-exploratory-summaries/ranks-ties-and-percentile-rank/
 * 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(Lesson037(), options));

static object Lesson037()
{
    double[] x = { 1, 2, 2, 4, 9 };
    double[] ranks = x.Select(v =>
    {
        int below = x.Count(y => y < v);
        int equal = x.Count(y => y == v);
        return below + (equal + 1) / 2.0;
    }).ToArray();
    double[] percentileRanks = ranks.Select(r => 100 * (r - 1) / (x.Length - 1)).ToArray();
    return new { ranks, percentileRanks };
}