Statistics Calculator (Mean, Median, Mode)
Analyze datasets with this advanced statistics tool. Calculate Mean, Median, Mode, Standard Deviation, and detect Outliers with step-by-step explanations.
About
Statistical analysis is the backbone of data interpretation, transforming raw numbers into actionable insights. Whether you are a student verifying a homework problem or a researcher examining a dataset distribution, understanding the central tendency (Mean, Median, Mode) and dispersion (Variance, Standard Deviation) is essential.
This tool goes beyond simple calculation. It acts as a pedagogical aid by showing "The Work" - a detailed, step-by-step breakdown of how each result was derived. It also employs the Interquartile Range (IQR) method to scientifically identify outliers - data points that differ significantly from other observations - helping you spot anomalies or errors in your data.
Formulas
The core formulas used in this calculator utilize the standard population and sample definitions.
Mean:
= ∑ xn
Standard Deviation (Population):
σ = √∑ (x − )2n
Outlier Detection (IQR Rule):
Low < Q1 − 1.5 × IQR
High > Q3 + 1.5 × IQR
Reference Data
| Statistic | Symbol | Definition | Use Case |
|---|---|---|---|
| Mean | The arithmetic average. | Data without outliers. | |
| Median | M | The middle value in a sorted list. | Skewed data (income, home prices). |
| Mode | Mo | The most frequent value. | Categorical data or voting. |
| Range | R | Difference between Max and Min. | Quick variability check. |
| Standard Deviation | σ | Average distance from the Mean. | Precision and risk analysis. |
| Variance | σ2 | Square of Standard Deviation. | Theoretical modeling. |