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A right-skewed box plot is a box plot whose upper side is stretched out: the median sits closer to the bottom of the box, and the upper whisker (often with a few outlier points above it) is longer than the lower one. This guide shows how to recognise a box plot skewed right, then works one dataset through by hand so you can see exactly where each feature comes from.
What a right-skewed box plot looks like
Three visual cues: (1) the median line is nearer the bottom edge of the box than the top, so the upper half of the box is longer; (2) the upper whisker is longer than the lower whisker; (3) points plotted individually above the upper whisker, which are values beyond the upper fence. In the language of the left-skewed versus right-skewed distribution guide, this is a long right tail: the NIST/SEMATECH e-Handbook says positive skewness values indicate data that are skewed right, meaning the right tail is long relative to the left tail.
Skewed right box plot versus box and whisker plot skewed right
These are the same thing. “Box plot”, “box-and-whisker plot” and “boxplot” all name the display built from the five-number summary, so a box and whisker plot skewed right and a right-skewed box plot are read identically.
Formula: the quartiles, IQR and fences behind the picture
Every feature above is computed from a handful of quantities. The NIST Handbook defines the lower quartile as the 25th percentile and the upper quartile as the 75th percentile, with the box representing the middle 50% of the data. OpenStax adds that each quarter of the data holds approximately 25% of the values.
- Q1, median, Q3: the 25th, 50th and 75th percentiles.
- IQR = Q3 – Q1: the length of the box.
- Lower fence L = Q1 – 1.5 x IQR; upper fence U = Q3 + 1.5 x IQR (NIST’s L1 and U1).
- Whiskers: drawn from the box to the smallest and largest observations that still lie inside the fences. Observations outside the fences are plotted as individual points.
Software differs on exactly how it computes Q1 and Q3; the box plots in R guide documents how fivenum() hinges and type-7 quantiles can draw slightly different boxes from the same data. The example below uses type-7 quantiles, which is what Excel’s QUARTILE.INC, R’s quantile() and NumPy’s percentile() return by default.
Worked example with the arithmetic shown
Eleven response times in seconds, already sorted: 3, 4, 4, 5, 6, 7, 8, 10, 12, 15, 38.
- Median: n = 11, so the median is the 6th value = 7.
- Q1: position 1 + 0.25 x (11 – 1) = 3.5, halfway between the 3rd value (4) and the 4th value (5): Q1 = 4.5.
- Q3: position 1 + 0.75 x 10 = 8.5, halfway between the 8th value (10) and the 9th (12): Q3 = 11.
- IQR: 11 – 4.5 = 6.5.
- Fences: lower = 4.5 – 1.5 x 6.5 = 4.5 – 9.75 = -5.25; upper = 11 + 9.75 = 20.75.
- Whiskers: the lowest value (3) is inside the lower fence, so the lower whisker ends at 3. The largest value inside 20.75 is 15, so the upper whisker ends at 15. The value 38 exceeds 20.75 and is plotted as an outlier.
- Mean: the sum is 3 + 4 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 15 + 38 = 112, and 112 / 11 = 10.18.
The picture follows from these numbers. The median-to-Q1 distance is 7 – 4.5 = 2.5, while the Q3-to-median distance is 11 – 7 = 4, so the median sits nearer the bottom of the box. The lower whisker is 4.5 – 3 = 1.5 long and the upper whisker is 15 – 11 = 4 long. One outlier sits above. The mean (10.18) exceeds the median (7), which OpenStax notes is often the case for right-skewed distributions.
Interpretation: how to read a box plot skewed right
| Feature | What you see | Reading |
|---|---|---|
| Median position | Nearer Q1 than Q3 (2.5 vs 4 in the example) | The lower half of the middle 50% is more tightly packed |
| Whiskers | Upper longer than lower (4 vs 1.5) | Values stretch further above the box than below it |
| Points above the upper whisker | One point at 38 | Value beyond the upper fence (20.75) |
| Mean versus median | 10.18 versus 7 | Mean pulled above the median; OpenStax says the mean is often greater than the median when data are skewed right |
Assumptions and common mistakes
- The box plot shows shape only through the five-number summary. It cannot show whether a distribution has two peaks. Check a histogram alongside it before describing the full shape.
- A long upper whisker is not always skew. In the example, one value (38) is the only point beyond the fence. Judge whether the long tail is one point or many before calling the whole distribution skewed.
- Small samples are unstable. With 11 observations, moving a single value can shift Q1 or Q3 and change which side looks longer.
- Different quartile methods shift the box. Report which method your software used.
- Do not delete flagged points automatically. An outlier above the fence is a prompt to check the data; see winsorizing versus trimming for handling options.
For the full distribution-shape discussion see normality of distribution, and for the quartile calculation itself the interquartile range and five-number summary guide.
How to report it
For skewed data, report the median with the interquartile range instead of (or beside) the mean and standard deviation. Example wording: “Response times were right-skewed (Mdn = 7.00 s, IQR = 6.50; Q1 = 4.50, Q3 = 11.00), with one value above the upper fence (38 s).” Name the quartile method you used.
How to calculate it in Excel, R or Python
Excel
=QUARTILE.INC(A1:A11,1) returns 4.5
=MEDIAN(A1:A11) returns 7
=QUARTILE.INC(A1:A11,3) returns 11
=AVERAGE(A1:A11) returns 10.18R
x <- c(3,4,4,5,6,7,8,10,12,15,38)
quantile(x, c(.25,.5,.75)) # 4.5 7.0 11.0
mean(x) # 10.18
boxplot(x, horizontal = TRUE)Python
import numpy as np
import matplotlib.pyplot as plt
x = [3,4,4,5,6,7,8,10,12,15,38]
q1, med, q3 = np.percentile(x, [25, 50, 75]) # 4.5 7.0 11.0
print(q1, med, q3, np.mean(x))
plt.boxplot(x, vert=False)
plt.show()Matplotlib’s and R’s default boxplot functions use their own whisker and quartile conventions, so the drawn box edges can differ slightly from the type-7 values printed above.
FAQ
How do you know if a box plot is skewed right?
Look for a median nearer the bottom of the box, a longer upper whisker, and possibly outlier points above it. Confirm with a histogram.
What does a box plot skewed right say about mean and median?
The mean is often greater than the median, as in the example (10.18 versus 7). OpenStax says “often”, not always.
Is a right-skewed box plot the same as a positively skewed one?
Yes. NIST states that positive skewness values indicate data skewed right, with a long right tail.
Can a box plot be skewed right with no outliers?
Yes. The upper whisker and upper half of the box can still be longer without any point exceeding the fence.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, Box Plot and Measures of Skewness (checked 2026-10-29).
- OpenStax, Introductory Statistics 2e, 2.4 Box Plots and 2.6 Skewness and the Mean, Median, and Mode (checked 2026-10-29).
