Calculator Input
Use the form below to paste numbers, upload a CSV file, choose a quartile method, and control display precision.
Example Data Table
This sample uses the exclusive median of halves method. You can load it into the form with one click.
| Observation | Value | Observation | Value | Observation | Value |
|---|---|---|---|---|---|
| 1 | 5 | 5 | 13 | 9 | 23 |
| 2 | 7 | 6 | 14 | 10 | 27 |
| 3 | 8 | 7 | 18 | 11 | 30 |
| 4 | 12 | 8 | 21 | Expected summary: 5, 8, 14, 23, 30 | |
Formula Used
Five-number summary consists of Minimum, First Quartile (Q1), Median, Third Quartile (Q3), and Maximum.
Range = Maximum − Minimum
Interquartile Range = Q3 − Q1
Lower Fence = Q1 − 1.5 × IQR
Upper Fence = Q3 + 1.5 × IQR
Outliers are values below the lower fence or above the upper fence. Quartiles depend on the chosen method: exclusive halves, inclusive halves, or linear interpolation.
How to Use This Calculator
Enter your values in the text area or upload a CSV file.
Choose the quartile method that matches your class, textbook, or reporting standard.
Set decimal precision for the displayed results.
Click the calculate button to show the result above the form.
Review the summary cards, detailed table, sorted dataset, and Plotly graph.
Use the CSV or PDF buttons to export your results.
Frequently Asked Questions
1. What does a five-number summary show?
It shows the minimum, Q1, median, Q3, and maximum. Together, these values summarize center, spread, and shape without requiring every raw observation to be reviewed individually.
2. Why can Q1 and Q3 change between tools?
Quartiles are not defined by one universal rule. Some tools use inclusive halves, others exclude the median, and some interpolate positions. This calculator lets you switch methods.
3. What is the IQR used for?
The interquartile range measures the spread of the middle fifty percent of your data. It is commonly used for box plots, variability checks, and outlier screening.
4. How are outliers identified here?
This page uses Tukey-style fences: values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are flagged as possible outliers.
5. Can I paste decimals and negative numbers?
Yes. The parser accepts integers, decimals, and negative numbers from pasted text or uploaded CSV files, as long as each entry is numeric.
6. Does the order of input values matter?
No. The calculator sorts the dataset automatically before computing quartiles, fences, and the five-number summary. You do not need to sort your values first.
7. What should I do if non-numeric text appears?
Non-numeric entries are ignored and counted in the results table. Remove labels, symbols, or mixed text if you want every cell to be used.
8. When should I use linear interpolation?
Use linear interpolation when your reporting standard defines quartiles as percentile positions between ranks. It is common in software, statistical packages, and analytics workflows.