Visualize data distribution through quartiles, whiskers, and outliers using box-and-whisker plots.
Last updated: April 2026
Minimum 5 values required
Box: IQR (Q1–Q3) | Line: Median | Whiskers: Range | Dots: Outliers
Count
11
Min
12.00
Q1 (25%)
20.00
Median
28.00
Q3 (75%)
38.50
Max
100.00
IQR
18.50
Outliers
1
Outliers Detected
100.00
Threshold: -7.75 to 66.25
| Component | Calculation | What It Means |
|---|---|---|
| Q1 (Lower Box Edge) | 25th percentile | 25% of data falls below this value |
| Median (Line in Box) | 50th percentile (Q2) | Middle value; 50% above, 50% below |
| Q3 (Upper Box Edge) | 75th percentile | 75% of data falls below this value |
| IQR (Box Width) | Q3 - Q1 | Spread of middle 50%; robust measure of variability |
| Whisker Lower | Q1 - 1.5×IQR (or min) | Lower boundary; beyond this = outlier |
| Whisker Upper | Q3 + 1.5×IQR (or max) | Upper boundary; beyond this = outlier |
| Outliers (Dots) | |value - Q1,Q3| > 1.5×IQR | Unusual points; often warrant investigation |
If median line is off-center, data is skewed. If whiskers are unequal, asymmetry exists. Compare multiple plots side-by-side to identify group differences.
A box plot (or box-and-whisker plot) is a standardized way of displaying the distribution of data using five key statistics: minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum.
What it shows: The box represents the middle 50% of data (IQR). The line inside shows the median. Whiskers extend to the edges of non-outlier data. Points beyond whiskers are outliers.
Data: 65, 72, 75, 78, 80, 82, 85, 88, 90, 92, 95, 100 (12 students)
Analysis:
The distribution is fairly symmetric with most scores clustering in the 76–91 range. The median (85) is close to center, indicating balanced distribution.
Box vs. whiskers?
Box shows IQR (middle 50% of data). Whiskers extend from box to farthest non-outlier values. Together they span 95% of typical data.
How are outliers determined?
Values beyond the fences = outliers. Lower fence = Q1 - 1.5×IQR; Upper fence = Q3 + 1.5×IQR. This rule flags ~0.7% of normal data as outliers.
Why 1.5×IQR specifically?
Balances sensitivity and specificity. Derived from normal distribution theory and widely adopted, but different multipliers work for different contexts.
Unequal whisker lengths?
Indicates skewness. Longer lower whisker = left-skewed; longer upper whisker = right-skewed. Equal whiskers = symmetric distribution.
Compare multiple datasets?
Yes! Create separate box plots for each. Side-by-side visualization reveals differences in location, spread, and outliers between groups.
Line inside the box?
That's the median (Q2). If off-center, data is skewed. If centered, symmetric. Its position shows where the middle value lies within the IQR.
Why IQR is useful?
Measures middle-50% variability—robust to outliers unlike standard deviation. Great for comparing spread across different distributions.
Minimum data points?
Box plots need at least 5 points for meaningful quartiles. Fewer points make quartile estimates unstable; consider other visualizations instead.
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