Formulae for stats

Here are some fundamental statistical formulae:

1. Mean (average) for a sample: x̄ = (Σ xᵢ) / n Where x̄ is the sample mean, Σ xᵢ is the sum of all data points, and n is the number of data points.

2. Median: The middle value in an ordered dataset. If there's an even number of data points, it's the average of the two middle values.

3. Mode: The value that appears most frequently in a dataset.

4. Range: The difference between the maximum and minimum values in a dataset. Range = Max Value - Min Value

5. Variance for a sample: s² = (Σ (xᵢ - x̄)²) / (n - 1) Where s² is the sample variance, xᵢ is each data point, x̄ is the sample mean, and n is the number of data points.

6. Standard Deviation for a sample: s = √(s²) = √( (Σ (xᵢ - x̄)²) / (n - 1) ) Where s is the sample standard deviation.

7. Z-score (standard score): z = (x - μ) / σ Where z is the z-score, x is the individual data point, μ is the population mean, and σ is the population standard deviation. (For a sample, you'd use x̄ and s instead of μ and σ).