Descriptive Statistics Calculator

Descriptive statistics rely on core mathematical formulas to outline the properties of a dataset. The arithmetic mean is calculated as the sum of all values divided by the total count (n): x̄ = (Σx) / n. The variance measures data spread around the mean; for a sample, it uses Bessel's correction with n - 1 in the denominator: s² = Σ(x - x̄)² / (n - 1). Standard deviation is simply the square root of the variance, bringing the unit of measurement back to the original scale of your data.

Imagine you have a small dataset representing test scores: 4, 8, 6, 5, 7. First, order the dataset from least to greatest: 4, 5, 6, 7, 8. The sample size (n) is 5. To find the mean, sum the values to get 30, then divide by 5, resulting in a mean of 6. The median is the middle value, which is 6. To calculate sample variance, find the squared differences from the mean: (4-6)² = 4, (5-6)² = 1, (6-6)² = 0, (7-6)² = 1, (8-6)² = 4. The sum of these squared deviations is 10. Dividing by n - 1 (which is 4) gives a sample variance of 2.5, and taking the square root yields a standard deviation of approximately 1.58.

Always inspect your dataset for outliers before calculating descriptive statistics, as extreme values can heavily skew the mean and variance. If your data contains significant outliers, reporting the median and interquartile range often provides a much truer picture of central tendency. Finally, always specify whether you are analyzing a complete population or a sample, as this changes the denominator used in your variance and standard deviation calculations.