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Statistics Calculator

5 Number Summary Calculator

Summarize any dataset instantly. The five-number summary provides a robust look at the spread and center of your data, helping you find quartiles, the median, and potential outliers.

5 Number Summary

Analyze distribution and spread of data

Results

Enter dataset to view summary

Understanding the 5 Number Summary

In descriptive statistics, a five-number summary simplifies a large block of numbers into five key markers: the minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum.

By looking at these values, you can instantly see the range, identify skewness, and prepare data for constructing box-and-whisker plots.

How outliers are detected

The Interquartile Range (IQR) represents the width of the middle 50% of your data.

IQR = Q3 − Q1

This calculator flags outliers automatically using the standard 1.5 × IQR rule. If a data point is below Q1 - (1.5 * IQR) or above Q3 + (1.5 * IQR), it is heavily skewed from the majority of the dataset.

How to use this tool

  • Type or paste your data set into the text box.
  • Numbers can be separated by commas, spaces, or line breaks.
  • The tool automatically ignores non-numeric characters and empty spaces.
  • The calculator returns the sorted dataset and highlights any outliers detected.

Example calculations

Example 1 — Small Dataset, No Outliers

Data: 1, 2, 5, 6, 7, 9, 12, 15

Sorted: 1, 2, 5, 6, 7, 9, 12, 15

Min = 1, Max = 15

Median (middle two 6, 7) = 6.5

Lower half: 1, 2, 5, 6 → Q1 = 3.5

Upper half: 7, 9, 12, 15 → Q3 = 10.5

Example 2 — Dataset With Outliers

Data: 10, 12, 15, 14, 13, 90

Sorted: 10, 12, 13, 14, 15, 90

Q1 = 12, Q3 = 15

IQR = 15 - 12 = 3

Upper limit = Q3 + (1.5 * 3) = 19.5

Since 90 > 19.5, 90 is an outlier.

Frequently Asked Questions

What is a 5 number summary?
It is a set of descriptive statistics that gives information about your dataset's center and spread. The five numbers are: Minimum, First Quartile (Q1), Median, Third Quartile (Q3), and Maximum.
How are quartiles calculated?
This calculator uses the exclusive method (common in TI-83 calculators and general statistics). First, find the median of the dataset. Then, find the median of the lower half (Q1) and upper half (Q3), excluding the main median from both halves if the count is odd.
What is the IQR?
The Interquartile Range (IQR) answers how spread out the middle 50% of your data is. It is calculated by subtracting Q1 from Q3 (IQR = Q3 - Q1).
How are outliers found?
Outliers are values that fall significantly outside the expected range. We use the 1.5 × IQR rule. Any value lower than (Q1 - 1.5 × IQR) or higher than (Q3 + 1.5 × IQR) is considered an outlier.

Assumptions & Reference Values

This tool returns estimates using standard financial formulas and the default parameters shown in the calculator inputs. Always consult a qualified financial advisor before making investment decisions.

Calculator Defaults:

  • Quartiles are calculated using the exclusive method (TI-83 / Moore and McCabe)
  • The median is excluded when selecting the lower and upper halves for Q1 and Q3
  • Outliers are computed using the 1.5 × IQR rule (values < Q1 - 1.5 IQR or > Q3 + 1.5 IQR)
  • Empty or non-numeric entries are skipped automatically

Disclaimer

All calculations are for informational purposes only. Past performance does not guarantee future results. Consult a licensed financial advisor for personalized advice.