Example Data Table
| Example Data |
Sorted Data |
Five-Number Summary |
| 12, 15, 18, 18, 21, 22, 25, 30, 35, 41, 44 |
12, 15, 18, 18, 21, 22, 25, 30, 35, 41, 44 |
Min 12, Q1 18, Median 22, Q3 35, Max 44 |
| 5, 7, 9, 10, 12, 18, 27, 30 |
5, 7, 9, 10, 12, 18, 27, 30 |
Min 5, Q1 8, Median 11, Q3 22.5, Max 30 |
Formula Used
The five-number summary is:
Minimum, Q1, Median, Q3, Maximum.
Range = Maximum - Minimum.
IQR = Q3 - Q1.
Lower fence = Q1 - multiplier × IQR.
Upper fence = Q3 + multiplier × IQR.
Values outside the fences are marked as possible outliers.
The calculator also shows Bowley skewness:
Bowley skewness = (Q3 + Q1 - 2 × Median) / IQR.
How to Use This Calculator
- Paste your numeric values into the data box.
- Separate values with commas, spaces, semicolons, or new lines.
- Select a quartile method that matches your course or report.
- Choose the number of decimal places.
- Adjust the outlier multiplier when needed.
- Add an optional unit label for clearer reports.
- Press Calculate Summary to see results above the form.
- Use the CSV or PDF buttons to download the report.
Understanding the Five-Number Summary
A five-number summary is a compact view of a data set. It shows the smallest value, first quartile, median, third quartile, and largest value. These five numbers explain center and spread quickly. They also prepare the data for a box plot. This calculator helps students, teachers, analysts, and researchers check those values without manual sorting.
Why This Summary Matters
Large lists can hide important patterns. The minimum and maximum show the full span. The median shows the middle location. The first and third quartiles divide the lower and upper parts. The interquartile range measures the middle spread. It is less affected by extreme values than the total range. That makes it useful when data has possible errors or unusual records.
Practical Data Review
Use the result to compare groups. A class score list can show whether most students performed closely. A delivery time list can show whether delays are common. A sales data set can show whether a few orders are unusually large. The outlier fences add another practical layer. They flag values below Q1 minus the chosen multiplier times IQR. They also flag values above Q3 plus that multiplier times IQR.
Advanced Options
Different books use different quartile rules. Some exclude the median from both halves. Some include it when the count is odd. Some use interpolated percentiles. This tool lets you select the rule. You can also set decimal places and an outlier multiplier. These options make the calculator useful for homework, reports, and quality checks.
Better Reporting
The download buttons save the same computed summary. The CSV file works well for spreadsheets. The PDF file is useful for quick sharing. The example table helps you verify the layout and meaning. Always review the sorted data before using the summary in a final report. A single mistyped number can change several values. Clean data gives stronger conclusions.
When to Use It
Use this summary before deeper modeling. It gives a fast check on distribution shape. It also supports clear explanations for nontechnical readers. When the median sits near one quartile, the data may be skewed. When the range is much larger than the IQR, extreme values may be influencing the data. Review them carefully.
FAQs
What is a five-number summary?
It is a compact statistical summary. It includes the minimum, first quartile, median, third quartile, and maximum. It helps describe spread and center quickly.
What does Q1 mean?
Q1 is the first quartile. It marks the value where about 25 percent of the data lies at or below that point.
What does Q3 mean?
Q3 is the third quartile. It marks the value where about 75 percent of the data lies at or below that point.
Why do quartile methods differ?
Textbooks and software sometimes split data differently. Some include the median in both halves. Others exclude it. Interpolation methods estimate quartiles between sorted positions.
What is IQR?
IQR means interquartile range. It equals Q3 minus Q1. It measures the spread of the middle half of the data.
How are outliers detected?
The calculator uses fences. The lower fence is Q1 minus multiplier times IQR. The upper fence is Q3 plus multiplier times IQR. Values outside them are flagged.
Can I use decimal data?
Yes. Enter whole numbers, decimals, or negative values. You can set decimal places to control how the final results are displayed.
What download formats are available?
You can download a CSV report for spreadsheets. You can also download a PDF report for printing, sharing, or storing with your analysis.