Measurement Error, Resolution, Accuracy, and Precision

/**
 * Fintech Math Bootcamp · Lesson 028 of 120
 * Measurement Error, Resolution, Accuracy, and Precision
 * Module 03: Data, Variables, Samples, and Measurement
 *
 * Scenario: A clock can be consistent and still wrong
 * Rule:     error = measured − reference
 *
 * Try it:   Does a small spread prove accuracy?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson028() {
  const reference = 100;
  const measured = [105, 105, 106, 104];
  const errors = measured.map(x => x - reference);
  const bias = errors.reduce((s,x) => s+x,0) / errors.length;
  const result = {errors, bias};
  return result;
}

export const checkedResult = {"errors":[5,5,6,4],"bias":5};

// Run this file directly: npx tsx lessons/03-data-variables-samples-and-measurement/028-measurement-error-resolution-accuracy-and-precision.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson028(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 028 of 120
Measurement Error, Resolution, Accuracy, and Precision
Module 03: Data, Variables, Samples, and Measurement

Scenario: A clock can be consistent and still wrong
Rule:     error = measured − reference

Try it:   Does a small spread prove accuracy?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json


def lesson028() -> dict:
    reference = 100
    measured = [105, 105, 106, 104]
    errors = [x - reference for x in measured]
    bias = sum(errors) / len(errors)
    result = {"errors": errors, "bias": bias}
    return result


if __name__ == "__main__":
    print(json.dumps(lesson028(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 028 of 120
 * Measurement Error, Resolution, Accuracy, and Precision
 * Module 03: Data, Variables, Samples, and Measurement
 *
 * Scenario: A clock can be consistent and still wrong
 * Rule:     error = measured − reference
 *
 * Try it:   Does a small spread prove accuracy?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

import java.util.Arrays;

public class Main {
    static final class MeasurementBias {
        final double[] errors;
        final double bias;

        MeasurementBias(double[] errors, double bias) {
            this.errors = errors;
            this.bias = bias;
        }
    }

    static MeasurementBias lesson028() {
        double reference = 100;
        double[] measured = {105, 105, 106, 104};
        double[] errors = Arrays.stream(measured).map(x -> x - reference).toArray();
        double bias = Arrays.stream(errors).reduce(0, (s, x) -> s + x) / errors.length;
        MeasurementBias result = new MeasurementBias(errors, bias);
        return result;
    }

    public static void main(String[] args) {
        MeasurementBias result = lesson028();
        System.out.println(object("errors", numbers(result.errors), "bias", num(result.bias)));
    }

    // Formats a double the way JSON.stringify does: whole numbers without ".0", null for NaN or infinity.
    static String num(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return String.valueOf((long) x);
        return String.valueOf(x);
    }

    static String quote(String text) {
        return "\"" + text.replace("\\", "\\\\").replace("\"", "\\\"") + "\"";
    }

    // Indents an already formatted JSON value by one level.
    static String nested(String json) {
        return json.replace("\n", "\n  ");
    }

    static String object(String... keysAndValues) {
        if (keysAndValues.length == 0) return "{}";
        StringBuilder out = new StringBuilder("{");
        for (int i = 0; i < keysAndValues.length; i += 2) {
            out.append(i == 0 ? "\n  " : ",\n  ")
               .append(quote(keysAndValues[i])).append(": ").append(nested(keysAndValues[i + 1]));
        }
        return out.append("\n}").toString();
    }

    static String array(java.util.List<String> items) {
        if (items.isEmpty()) return "[]";
        StringBuilder out = new StringBuilder("[");
        for (int i = 0; i < items.size(); i++) {
            out.append(i == 0 ? "\n  " : ",\n  ").append(nested(items.get(i)));
        }
        return out.append("\n]").toString();
    }

    static String numbers(double... values) {
        java.util.List<String> items = new java.util.ArrayList<String>();
        for (double value : values) items.add(num(value));
        return array(items);
    }
}

// Fintech Math Bootcamp · Lesson 028 of 120
// Measurement Error, Resolution, Accuracy, and Precision
// Module 03: Data, Variables, Samples, and Measurement
//
// Scenario: A clock can be consistent and still wrong
// Rule:     error = measured − reference
//
// Try it:   Does a small spread prove accuracy?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run it: go run main.go

package main

import (
	"encoding/json"
	"fmt"
)

type MeasurementBias struct {
	Errors []float64 `json:"errors"`
	Bias   float64   `json:"bias"`
}

func lesson028() MeasurementBias {
	reference := 100.0
	measured := []float64{105, 105, 106, 104}
	errors := make([]float64, len(measured))
	for i, x := range measured {
		errors[i] = x - reference
	}
	sum := 0.0
	for _, x := range errors {
		sum += x
	}
	bias := sum / float64(len(errors))
	result := MeasurementBias{Errors: errors, Bias: bias}
	return result
}

func main() {
	printJSON(lesson028())
}

// printJSON prints a value as JSON indented with two spaces, like JSON.stringify(value, null, 2).
func printJSON(value any) {
	out, err := json.MarshalIndent(value, "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 028 of 120
 * Measurement Error, Resolution, Accuracy, and Precision
 * Module 03: Data, Variables, Samples, and Measurement
 *
 * Scenario: A clock can be consistent and still wrong
 * Rule:     error = measured − reference
 *
 * Try it:   Does a small spread prove accuracy?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: g++ -std=c++17 -o main main.cpp && ./main
 */

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

// Formats a double the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
std::string num(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    auto [end, error] = std::to_chars(buffer, buffer + sizeof buffer, x);
    (void)error;
    return std::string(buffer, end);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') out += '\\';
        out += c;
    }
    return out + "\"";
}

// Indents an already formatted JSON value by one level.
std::string nested(const std::string& json) {
    std::string out;
    for (char c : json) {
        out += c;
        if (c == '\n') out += "  ";
    }
    return out;
}

std::string object(const std::vector<std::pair<std::string, std::string>>& fields) {
    if (fields.empty()) return "{}";
    std::string out = "{";
    for (std::size_t i = 0; i < fields.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += quote(fields[i].first) + ": " + nested(fields[i].second);
    }
    return out + "\n}";
}

std::string array(const std::vector<std::string>& items) {
    if (items.empty()) return "[]";
    std::string out = "[";
    for (std::size_t i = 0; i < items.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += nested(items[i]);
    }
    return out + "\n]";
}

std::string numbers(const std::vector<double>& values) {
    std::vector<std::string> items;
    for (double value : values) items.push_back(num(value));
    return array(items);
}

struct MeasurementBias {
    std::vector<double> errors;
    double bias;
};

MeasurementBias lesson028() {
    const double reference = 100;
    const std::vector<double> measured{105, 105, 106, 104};
    std::vector<double> errors;
    for (double x : measured) errors.push_back(x - reference);
    const double bias = std::accumulate(errors.begin(), errors.end(), 0.0) / errors.size();
    const MeasurementBias result{errors, bias};
    return result;
}

int main() {
    const MeasurementBias result = lesson028();
    std::cout << object({{"errors", numbers(result.errors)}, {"bias", num(result.bias)}}) << "\n";
}

//! Fintech Math Bootcamp · Lesson 028 of 120
//! Measurement Error, Resolution, Accuracy, and Precision
//! Module 03: Data, Variables, Samples, and Measurement
//!
//! Scenario: A clock can be consistent and still wrong
//! Rule:     error = measured − reference
//!
//! Try it:   Does a small spread prove accuracy?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct MeasurementBias {
    errors: Vec<f64>,
    bias: f64,
}

fn lesson028() -> MeasurementBias {
    let reference = 100.0;
    let measured = [105.0, 105.0, 106.0, 104.0];
    let errors: Vec<f64> = measured.iter().map(|&x| x - reference).collect();
    let bias = errors.iter().fold(0.0, |s, &x| s + x) / errors.len() as f64;
    let result = MeasurementBias { errors, bias };
    result
}

fn main() {
    let result = lesson028();
    println!(
        "{}",
        object(&[("errors", numbers(&result.errors)), ("bias", num(result.bias))])
    );
}

/// Formats a number the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
fn num(x: f64) -> String {
    if x.is_finite() {
        format!("{}", x)
    } else {
        "null".to_string()
    }
}

fn quote(text: &str) -> String {
    format!("\"{}\"", text.replace('\\', "\\\\").replace('"', "\\\""))
}

/// Indents an already formatted JSON value by one level.
fn nested(json: &str) -> String {
    json.replace('\n', "\n  ")
}

fn object(fields: &[(&str, String)]) -> String {
    if fields.is_empty() {
        return "{}".to_string();
    }
    let lines: Vec<String> = fields
        .iter()
        .map(|(key, value)| format!("  {}: {}", quote(key), nested(value)))
        .collect();
    format!("{{\n{}\n}}", lines.join(",\n"))
}

fn array(items: &[String]) -> String {
    if items.is_empty() {
        return "[]".to_string();
    }
    let lines: Vec<String> = items.iter().map(|item| format!("  {}", nested(item))).collect();
    format!("[\n{}\n]", lines.join(",\n"))
}

fn numbers(values: &[f64]) -> String {
    let items: Vec<String> = values.iter().map(|&value| num(value)).collect();
    array(&items)
}

/**
 * Fintech Math Bootcamp · Lesson 028 of 120
 * Measurement Error, Resolution, Accuracy, and Precision
 * Module 03: Data, Variables, Samples, and Measurement
 *
 * Scenario: A clock can be consistent and still wrong
 * Rule:     error = measured − reference
 *
 * Try it:   Does a small spread prove accuracy?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/data-variables-samples-and-measurement/measurement-error-resolution-accuracy-and-precision/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: dotnet run  (inside a console project that holds this Program.cs)
 */

using System.Text.Json;

var jsonOptions = new JsonSerializerOptions { WriteIndented = true, PropertyNamingPolicy = JsonNamingPolicy.CamelCase };
Console.WriteLine(JsonSerializer.Serialize(Lesson028(), jsonOptions));

static MeasurementBias Lesson028()
{
    const double reference = 100;
    double[] measured = { 105, 105, 106, 104 };
    var errors = measured.Select(x => x - reference).ToArray();
    var bias = errors.Aggregate(0.0, (s, x) => s + x) / errors.Length;
    var result = new MeasurementBias(errors, bias);
    return result;
}

record MeasurementBias(double[] Errors, double Bias);