5 Number Summary Calculator
Calculate the five-number summary of your dataset including quartiles
Table of Contents
How to Use
- Enter your data values separated by commas, spaces, or semicolons
- Click calculate to compute the five-number summary
- Review the minimum, Q1, median, Q3, maximum, range, and IQR
What is the Five-Number Summary?
The five-number summary is a descriptive statistic that provides information about a dataset using five key values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
These five numbers divide the dataset into four equal parts, with 25% of the data falling between each consecutive pair of values. This summary is the basis for creating box plots (box-and-whisker plots).
Components of the Five-Number Summary
- Minimum: The smallest value in the dataset
- Q1 (First Quartile): The median of the lower half of the data (25th percentile)
- Median (Q2): The middle value that divides the dataset in half (50th percentile)
- Q3 (Third Quartile): The median of the upper half of the data (75th percentile)
- Maximum: The largest value in the dataset
Additional Measures
In addition to the five-number summary, this calculator provides:
- Range: The difference between the maximum and minimum values, showing the spread of the entire dataset
- IQR (Interquartile Range): The difference between Q3 and Q1, representing the middle 50% of the data and used to identify outliers
Applications
- Creating box plots for visual data representation
- Comparing distributions between different datasets
- Identifying outliers using the IQR method
- Understanding data spread and central tendency
- Quality control in manufacturing
- Academic research and data analysis
Frequently Asked Questions
- What is the difference between median and Q2?
- The median and Q2 (second quartile) are the same value. Both represent the middle point of the dataset where 50% of values fall below and 50% fall above.
- How is the IQR used to detect outliers?
- Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are typically considered outliers. This is a common method in box plot analysis.
- Can I use this calculator for small datasets?
- Yes, you need at least 2 values, though the five-number summary is most informative with larger datasets (typically 10 or more values).
- What if my dataset has an even number of values?
- The calculator uses interpolation to find quartiles when needed. For even datasets, the median is the average of the two middle values.