The Box Plot Calculator computes the five-number summary (minimum, Q1, median, Q3, maximum), IQR, and identifies outliers using the 1.5×IQR rule. Box plots reveal distribution shape, spread, skew, and outliers at a glance — more informative than mean and standard deviation alone.
8
15
28.5
39
60
24
52
-21
75
8
15
28.5
39
60
24
52
-21
75
A mean tells you the center of a dataset. A box plot tells you the shape of the whole distribution in 5 numbers — revealing whether data is symmetric, skewed left or right, tightly clustered or widely spread, and whether extreme outliers are distorting your summary statistics. The box plot calculator computes the complete five-number summary and flags any outliers using the standard 1.5×IQR criterion.
Interquartile Range (IQR) = Q3 − Q1 — the range of the middle 50% of data, resistant to outliers. Outlier fences: Lower = Q1 − 1.5 × IQR; Upper = Q3 + 1.5 × IQR. Any value outside these fences is marked as an outlier. Use this online calculator for your dataset. The normal distribution calculator provides complementary statistical analysis tools.
The box spans Q1 to Q3 (the IQR); the line inside the box is the median; whiskers extend to the most extreme values within the 1.5×IQR fences; individual dots mark outliers. Interpreting shape: if the median line is centered in the box — symmetric distribution; if median is closer to Q1 — right-skewed (long upper tail); if median is closer to Q3 — left-skewed (long lower tail). Long whiskers indicate high variability; a narrow box with long whiskers suggests many moderate values with occasional extremes; a wide box indicates high variability in the middle 50% of data.
Box plots excel at: comparing distributions across groups (e.g., test scores by school, salaries by department); identifying outliers; showing skewness; comparing medians across categories. They are less informative for: bimodal distributions (a bimodal dataset might have a misleadingly simple-looking box plot); very small samples (box plots need at least 5–10 values to be meaningful). The statistics calculators provide the complete statistical analysis toolkit.
Examine the box plot's components systematically: (1) The median line shows the center — is it near the middle of the box or shifted toward Q1 or Q3? A shifted median indicates skewness. (2) The box width (IQR) shows central spread — a narrow box means the middle 50% is tightly clustered. (3) Whisker lengths reveal tail behavior — one whisker much longer than the other indicates skewness. (4) Outlier dots beyond the fences flag unusual values requiring investigation.
A perfectly symmetric distribution would show the median centered in the box, with equal whisker lengths and equal gaps from the fences to the extremes. Most real-world data shows some degree of asymmetry.
Inputs
Results
The box spans 42K to 60K with median at 50K. The IQR of 18K shows moderate spread. The upper fence is 87K, meaning the 120K salary is an outlier — likely an executive among regular employees.
Inputs
Results
A nearly symmetric distribution: median 21 is centered in the box (17 to 25). Both whiskers are of similar length. No outliers — all values fall within the fences [5, 37]. This suggests uniform growth conditions.
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