Calculating Variance in Rust

Variance is a statistical measure of the spread of data around its mean. Implementing a function to calculate variance is a fundamental task in data analysis and machine learning. This challenge asks you to write a Rust function that accurately computes the variance of a given slice of floating-point numbers.

Problem Description

You are tasked with creating a Rust function named calculate_variance that takes a slice of f64 (64-bit floating-point numbers) as input and returns the variance of the data. The variance is calculated as the average of the squared differences from the mean.

Key Requirements:

• The function must handle empty input slices gracefully, returning 0.0 in such cases.
• The function must correctly calculate the mean of the input data.
• The function must correctly calculate the squared differences from the mean.
• The function must correctly calculate the average of the squared differences (variance).
• The function should be efficient and avoid unnecessary allocations.

Expected Behavior:

The function should return a f64 representing the variance of the input data. The result should be accurate to a reasonable degree, considering the limitations of floating-point arithmetic.

Edge Cases to Consider:

• Empty input slice.
• Slice containing only one element (variance should be 0.0).
• Slice containing very large or very small numbers (potential for overflow/underflow).
• Slice containing a mix of positive and negative numbers.

Examples

Example 1:

Input: [1.0, 2.0, 3.0, 4.0, 5.0]
Output: 2.0
Explanation: The mean is (1+2+3+4+5)/5 = 3.0. The squared differences are (1-3)^2, (2-3)^2, (3-3)^2, (4-3)^2, (5-3)^2, which are 4, 1, 0, 1, 4. The variance is (4+1+0+1+4)/5 = 2.0.

Example 2:

Input: [2.5, 2.5, 2.5, 2.5, 2.5]
Output: 0.0
Explanation: The mean is 2.5. All the values are equal to the mean, so the squared differences are all 0. The variance is 0.0.

Example 3:

Input: []
Output: 0.0
Explanation: The input slice is empty. The variance is defined as 0.0 in this case.

Constraints

• The input slice will contain only f64 values.
• The length of the input slice can be between 0 and 1000 (inclusive).
• The f64 values in the input slice can range from -1000.0 to 1000.0.
• The function should complete within 100 milliseconds for any valid input.

Notes

• Consider using Rust's built-in functions for summing the elements of the slice to improve efficiency.
• Be mindful of potential floating-point precision issues when calculating the mean and variance.
• Think about how to handle the edge case of an empty input slice to avoid division by zero errors.
• The variance formula is: variance = Σ(xᵢ - μ)² / N, where xᵢ is each data point, μ is the mean, and N is the number of data points.