Statistics Calculator

Descriptive Statistics Explained

Descriptive statistics summarize and describe the key features of a dataset. Enter your numbers separated by commas, spaces, or newlines, and this calculator instantly computes all major descriptive statistics.

Mean (arithmetic average) is the sum divided by count. Median is the middle value when sorted. Mode is the most frequently occurring value. Standard deviation measures how spread out values are from the mean.

Key Statistical Formulas

Mean = Σx / n Median = middle value of sorted data Variance σ² = Σ(x − mean)² / n Standard Deviation σ = √Variance Range = Max − Min

When to Use Each Statistic

Statistic	Best For	Weakness
Mean	Symmetric data, normal distributions	Sensitive to outliers
Median	Skewed data, income, home prices	Ignores extreme values
Mode	Categorical data, most common value	May not exist or be unique
Std Dev	Measuring spread and variability	Same units as data

Frequently Asked Questions

Population standard deviation (σ) divides by n and describes the entire population. Sample standard deviation (s) divides by n−1 (Bessel's correction) and estimates the population from a sample. This calculator uses population standard deviation. For sample standard deviation, divide the variance by n−1 instead of n.

Standard deviation measures the average distance of data points from the mean. A small SD means data is clustered closely around the mean; a large SD means data is spread out. In a normal distribution, 68% of values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs (the 68-95-99.7 rule).

Mean income is skewed upward by extremely high earners. A small number of billionaires dramatically raises the mean while most people's incomes are near the median. The median (middle value) is resistant to extreme outliers and better represents a 'typical' income. This is why government reports typically use median household income.

An outlier is a data point significantly distant from other values. Outliers can dramatically affect mean and standard deviation while having minimal effect on the median. Common rules for identifying outliers include the IQR method (values more than 1.5× the interquartile range beyond Q1 or Q3) or the Z-score method (values more than 3 standard deviations from the mean).