Enter data and choose options
Formula used
min(x₁, x₂, ..., xₙ)Range = Maximum − Minimumz = (xₘᵢₙ − mean) ÷ standard deviationQ₁ − 1.5 × IQRσ² = Σ(x − μ)² ÷ Ns² = Σ(x − x̄)² ÷ (n − 1)How to use this calculator
- Enter numeric values in the primary dataset field.
- Select the calculation mode matching your analysis.
- Add optional labels, categories, dates, or frequencies.
- Apply thresholds and filters when they are needed.
- Choose sample or population variance calculations.
- Press calculate to view statistics and charts.
- Copy, print, or export the finished results.
Worked example
The dataset contains 8, 3, 12, 5, and 3. The smallest observed value is three. It appears twice within the complete five-value dataset here.
| Dataset | Minimum | Maximum | Range |
|---|---|---|---|
| 8, 3, 12, 5 | 3 | 12 | 9 |
| -4, 2, -9, 7 | -9 | 7 | 16 |
| 0, 0, 6, 10 | 0 | 10 | 10 |
| 2.5, 1.2, 4.8 | 1.2 | 4.8 | 3.6 |
Understanding minimum statistics
What the minimum represents
The minimum is the smallest observed numerical value. It marks the dataset's lower endpoint. This endpoint helps summarize spread and potential extremes clearly.
Minimum versus lower quartile
The minimum uses only the lowest observation. The lower quartile describes the lower data region. Quartiles usually resist isolated extremes better than minimums do.
Minimum values and outliers
A very small value may be unusual. The IQR rule provides a practical screening boundary. Context should always guide the final outlier decision carefully.
Duplicate minimum values
Several observations can share the same minimum. Frequency shows how often that value appears. Positions reveal every matching record in original order clearly.
Frequently asked questions
What is a minimum in statistics?
It is the smallest observed dataset value. It defines the dataset's lower endpoint. Analysts use it when describing overall data spread clearly.
Can a minimum be negative?
Yes, negative values can be valid observations. The smallest negative number becomes the minimum. Filters exclude negatives when your analysis requires that choice.
How are duplicate minimums handled?
Every matching minimum remains part of calculations. The calculator reports frequency and original positions. Duplicate values also affect percentages and grouped count totals.
What is the minimum positive value?
It is the smallest number above zero. Negative values and zero are excluded. This mode helps analyze strictly positive measurements safely online.
What does minimum absolute value mean?
It identifies values closest to zero. The original signs remain visible afterward. Equal distances can produce several matching minimums together simultaneously.
How is a lower outlier detected?
The calculator uses the standard IQR boundary. Values below Q1 minus 1.5 IQR qualify. Domain knowledge should confirm whether removal is appropriate carefully.
Should I choose sample or population variance?
Use population variance for complete populations. Use sample variance for population estimates. Sample variance requires at least two valid observations here.
Can I calculate grouped data?
Yes, provide one frequency per entered value. Frequencies must be positive whole numbers. The calculator expands them before computing complete statistics accurately.
Can CSV data be uploaded?
Yes, upload a standard CSV file. Numeric first-column values become the primary dataset. Headers and nonnumeric first-column entries are skipped automatically safely.