Statistics Calculator
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Descriptive Statistics Reference
| Measure | Description |
|---|---|
| Mean | Sum of all values ÷ count (arithmetic average) |
| Median | Middle value when sorted; average of two middles for even n |
| Mode | Most frequently occurring value(s) |
| Range | Max − Min |
| Variance (pop.) | Average squared deviation from the mean |
| Std Dev (pop.) | Square root of variance — spread around the mean |
| Std Dev (sample) | Uses n−1 denominator (Bessel's correction) |
| IQR | Q3 − Q1 (interquartile range — middle 50% spread) |
Population vs Sample Standard Deviation
Use population SD (σ) when your data represents the entire group — for example, exam scores for every student in one class. Use sample SD (s) when your data is a subset drawn from a larger population — for example, a survey of 200 people representing millions. Sample SD uses n−1 in the denominator (Bessel's correction) to correct for the tendency of a small sample to underestimate true variability. Most real-world analysis uses sample SD.
When to Use Mean vs Median
The mean works best for symmetric distributions without extreme outliers — it incorporates every value in the calculation. The median is more robust when data is skewed or contains outliers. Average household income is a classic example: a handful of billionaires pull the mean far above what a typical household earns, while the median stays near the middle. Rule of thumb: if mean and median are close, either works; if they diverge significantly, use median and investigate the outliers.
Detecting Outliers With IQR
The IQR (Q3 − Q1) is used to identify potential outliers without being influenced by extreme values. The standard rule: values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are outliers — this is the method used in standard box plots. Outliers may be data entry errors, genuinely extreme measurements, or a different population mixed into your dataset. Always investigate outliers before removing them; removing valid data distorts your results.