Box Plot Calculator - Calculate Five-Number Summary
Calculate quartiles, median, IQR, and identify outliers in your dataset with instant five-number summary and box plot statistics
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Five-Number Summary
Detailed Statistics
What is a Box Plot Calculator?
A Box Plot Calculator computes the five-number summary of a dataset, including minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
This calculator is used for:
- Data Distribution - Visualize data spread and central tendency
- Outlier Detection - Identify unusual values in datasets
- Comparative Analysis - Compare multiple datasets side by side
- Statistical Summary - Quick overview of data characteristics
To create another visual representation of your data, explore our Histogram Calculator to display frequency distributions with customizable bin widths.
To understand the spread of data in a normal distribution, check out our Empirical Rule Calculator to see what percentage of data falls within standard deviations of the mean.
To organize your data into categories and frequencies, visit our Frequency Distribution Calculator to create organized tables showing how often values occur.
To visualize data points individually on a number line, use our Dot Plot Calculator to create simple plots showing each value in your dataset.
How Box Plots Work
Box plot calculations follow these steps:
The box represents the middle 50% of data, whiskers extend to the minimum and maximum non-outlier values.
Key Concepts Explained
Quartiles
Q1, Q2, Q3 divide data into four equal parts. Q1 is the 25th percentile, Q2 is the median, and Q3 is the 75th percentile.
Interquartile Range (IQR)
The IQR measures the middle 50% of data spread. It's robust to outliers and used to identify extreme values.
Outlier Detection
Values beyond the fences (Q1 - 1.5×IQR or Q3 + 1.5×IQR) are considered outliers and require investigation.
How to Use This Calculator
Enter Your Data
Input numbers separated by commas or spaces
Click Calculate
Get instant five-number summary and statistics
Review Results
Analyze quartiles, IQR, outliers, and distribution
Benefits of This Calculator
- Complete Analysis - All box plot statistics in one place
- Outlier Detection - Automatic identification of extreme values
- Instant Results - Immediate statistical calculations
- Educational Tool - Learn about data distribution
- Research Ready - Professional statistical analysis
- Free Access - No registration required
Factors Affecting Results
- Sample Size - Larger samples provide more reliable quartiles
- Data Distribution - Skewed data affects box plot shape
- Outliers - Extreme values influence whisker positions
- Data Type - Works best with continuous numerical data
- Quartile Method - Different calculation methods may vary slightly
- Data Sorting - Data must be ordered for accurate calculations
Frequently Asked Questions
What is a box plot?
A box plot (box-and-whisker plot) is a graphical representation of data distribution showing the median, quartiles, and outliers. It displays the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
How do you calculate quartiles for a box plot?
Quartiles divide sorted data into four equal parts. Q1 is the median of the lower half, Q2 is the overall median, and Q3 is the median of the upper half. The interquartile range (IQR) is Q3 - Q1.
What is the interquartile range (IQR)?
The interquartile range (IQR) is the difference between the third quartile (Q3) and first quartile (Q1). It represents the middle 50% of the data and is a measure of statistical dispersion.
How are outliers identified in a box plot?
Outliers are data points that fall below Q1 - 1.5×IQR or above Q3 + 1.5×IQR. These are values that are significantly different from the rest of the data.
What does a box plot show?
A box plot shows the data distribution, central tendency (median), spread (IQR), skewness, and identifies potential outliers. It's useful for comparing multiple datasets and understanding data variability.
When should you use a box plot?
Use box plots when comparing multiple groups, identifying outliers, displaying data distribution, showing variability, or when you want to see the five-number summary of your data at a glance.