Statistics From Scratch

Implement fundamental statistical functions from scratch. These are essential for understanding data and building ML models.

Functions to implement

1. mean(data)

Compute the arithmetic mean (average).

• Input: A list of numbers
• Output: The sum divided by the count

2. variance(data, population=True)

Compute the variance.

• Input: A list of numbers, and whether to use population variance
• Output: Average squared deviation from mean
• Population variance divides by n, sample variance divides by (n-1)

3. std(data, population=True)

Compute the standard deviation.

• Input: A list of numbers, and whether to use population std
• Output: Square root of variance

4. median(data)

Compute the median (middle value).

• Input: A list of numbers
• Output: The middle value (or average of two middle values)

5. correlation(x, y)

Compute the Pearson correlation coefficient.

• Input: Two lists of numbers of equal length
• Output: A value between -1 and 1

Examples

mean([1, 2, 3, 4, 5])         # 3.0
variance([1, 2, 3, 4, 5])     # 2.0 (population)
std([1, 2, 3, 4, 5])          # ~1.41
median([1, 2, 3, 4, 5])       # 3
median([1, 2, 3, 4])          # 2.5
correlation([1, 2, 3], [1, 2, 3])  # 1.0 (perfect positive)

Input domain and boundary policy

Inputs are nonempty lists of finite numbers. Sample variance/std require at least two observations; population variance/std allow one. Correlation inputs have equal nonzero length. Return 0.0 if either correlation input is constant (the mathematical coefficient is undefined, so this is an API sentinel). Do not mutate either input, including when finding the median. Empty inputs, mismatched lengths, and non-finite values are outside this exercise's domain.