Variance

The variance is a measure of how far spread out the values in a dataset are from the mean. It quantifies the amount of variation or dispersion present in the data.

A higher variance indicates values are more spread out from the mean, while lower variance indicates they are clustered closely around the mean.

Variance is computed as the average of squared deviations from mean. Standard deviation is the square root of variance.

Understanding variance helps analyze the distribution of data.

Solution

Here is how variance can be calculated:

Java

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double variance(double[] data) {
  double mean = findMean(data);
  double sumSq = 0;

  for(double n : data) {
    sumSq += (n - mean)*(n - mean);
  }

  return sumSq / data.length;
}

C++

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double variance(vector<double> data) {
  double mean = findMean(data);
  double sumSq = 0;

  for(double n : data) {
    sumSq += (n - mean) * (n - mean); 
  }

  return sumSq / data.size();
}

Python

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from statistics import mean

def variance(data):
  mu = mean(data)
  sum_sq = sum((x - mu)**2 for x in data)

  return sum_sq / len(data)

Variance measures how spread out data is from the mean. Higher variance indicates greater dispersion.

Description: Variance

Variance is a statistical measure that represents the dispersion or spread of a set of numbers. A high variance indicates that the numbers in the set are far from the mean, while a low variance suggests that they are close to the mean. Mathematically, variance is calculated as the average of the squared differences from the mean. It is often denoted by ( \sigma^2 ).

Solution:

Below are implementations of how to calculate the variance of an array of numbers in Java, C++, and Python.

Java

In Java, we can use loops and basic arithmetic operations to calculate variance.

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public class VarianceExample {
    public static double variance(int[] numbers) {
        int sum = 0;
        for (int num : numbers) {
            sum += num;
        }
        double mean = (double) sum / numbers.length;

        double variance = 0;
        for (int num : numbers) {
            variance += Math.pow((num - mean), 2);
        }
        return variance / numbers.length;
    }

    public static void main(String[] args) {
        int[] numbers = {1, 2, 3, 4, 5};
        System.out.println("Variance: " + variance(numbers));
    }
}

C++

In C++, we can make use of the <algorithm> and <cmath> libraries.

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#include <iostream>
#include <vector>
#include <cmath>
#include <numeric>

double variance(const std::vector<int>& numbers) {
    double sum = std::accumulate(numbers.begin(), numbers.end(), 0);
    double mean = sum / numbers.size();

    double variance = 0;
    for (int num : numbers) {
        variance += std::pow((num - mean), 2);
    }
    return variance / numbers.size();
}

int main() {
    std::vector<int> numbers = {1, 2, 3, 4, 5};
    std::cout << "Variance: " << variance(numbers) << std::endl;
    return 0;
}

Python

Python provides a straightforward and easy-to-understand way to calculate variance.

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def variance(numbers):
    mean = sum(numbers) / len(numbers)
    variance = sum((x - mean) ** 2 for x in numbers) / len(numbers)
    return variance

numbers = [1, 2, 3, 4, 5]
print("Variance:", variance(numbers))

Key Takeaways

Variance measures the dispersion of a set of numbers.
It is calculated as the average of the squared differences from the mean.
Java, C++, and Python implementations are straightforward, involving summing, squaring, and dividing.
Libraries like <cmath> in C++ and math in Python can be handy but are not strictly required for this basic calculation.