Right-Skewed Histogram: How to Read, Compute and Report It

A right-skewed histogram has its tallest bars toward the left and a long tail stretching to the right. It is also called a positively skewed histogram, a skewed right histogram or a histogram skewed right. The word “right” names the side of the tail, not the side where the bars pile up. This guide shows how to recognise the shape, compute the skewness coefficient step by step, and report the result.

Definition: what a right-skewed histogram looks like

A histogram summarises one variable by splitting its range into equal-sized bins and counting how many observations fall in each (NIST/SEMATECH e-Handbook, section 1.3.3.14). NIST lists “skewed (non-symmetric) right” as one of the shapes a histogram can show. In a right-skewed histogram the bars peak near the low end and then taper off slowly toward the high values. OpenStax describes its right-skewed example the same way: “It is skewed to the right.” Its figure description reads, “The peak is to the left, and the heights of the bars taper down to the right.”

Typical sources are measures bounded below by zero with an occasional very large value, such as waiting times, counts of events or response delays. The few large values form the long right tail.

Right-skewed histogram, right skewed histogram, skewed right histogram: the same shape

These phrases, along with “histogram skewed right” and “positively skewed”, all describe one shape: a long right tail and a positive skewness coefficient. The hyphen and the word order change nothing. For the mirror image, with the peak on the right and the tail on the left, see the left-skewed histogram guide. For a general comparison of both directions, see left-skewed vs right-skewed distributions.

Skewed right histogram vs histogram skewed right

There is no difference in meaning. Some authors write “skewed to the right”, others “right-skewed” or “positively skewed”. Pick one term for a paper and use it consistently.

Formula: skewness g₁ and why it is positive

NIST gives the moment coefficient of skewness for data Y₁, Y₂, …, Y_N as:

g₁ = [ Σ(Y_i − Ȳ)³ / N ] / s³

• Y_i: the i-th observation.
• Ȳ: the sample mean.
• N: the number of observations.
• s: the standard deviation, computed with N (not N − 1) in the denominator, as NIST notes for this formula.
• Σ: the sum over all N observations.

NIST states that “positive values for the skewness indicate data that are skewed right.” The reason is the cube. The few large values lie far above the mean, so their cubed deviations are large and positive and outweigh the many small negative deviations on the low side. For both directions side by side, see the left-skewed vs right-skewed guide linked above.

Worked example: 20 response times

An illustrative dataset (invented for this example, not real data) of 20 response times in days, sorted: 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9, 10, 12, 14, 17, 21, 30.

Step 1: the histogram counts (bins of width 5, each bin includes its lower edge)

Bin (days)	0–4	5–9	10–14	15–19	20–24	25–29	30–34
Count	5	9	3	1	1	0	1

The counts add to 20. The tallest bar (5–9) sits at the left and the bars thin out toward 30: a right-skewed shape.

Step 2: mean, median, mode, spread

• Mean: 178 / 20 = 8.9.
• Median: the 10th and 11th sorted values are 6 and 7, so the median is (6 + 7) / 2 = 6.5.
• Mode: the value 5 occurs three times, more than any other, so the mode is 5.
• Quartiles (inclusive method): Q1 = 4.75 and Q3 = 10.5, so IQR = 5.75.
• Sum of squared deviations = 929.8. Divided by N = 20 this gives 46.49, so s = √46.49 = 6.818. With N − 1 the standard deviation is √(929.8 / 19) = 6.995, about 7.00.

Step 3: skewness

The cubed deviations from the mean sum to 10,644.96. Dividing by N gives 532.248. The cube of s is 6.8184³ ≈ 316.985. So g₁ = 532.248 / 316.985 = 1.68.

The positive sign agrees with the picture. The mean (8.9) sits above the median (6.5), pulled toward the tail by the 21-day and 30-day values. Software that applies a small-sample adjustment, such as Excel’s SKEW or scipy.stats.skew(…, bias=False), reports 1.82 for the same data. State which version you used.

Reading a histogram skewed right: mean, median and mode

For its right-skewed example, OpenStax notes: “Of the three statistics, the mean is the largest, while the mode is the smallest.” It also hedges: “When the distribution is skewed to the right, the mean is often greater than the median.” Treat the ordering as a tendency, not a law. In the worked example, mode 5 < median 6.5 < mean 8.9 shows the typical pattern.

What you see or compute	What it indicates	Source
Peak at the low end, long tail to the right	Skewed right (positively skewed)	NIST 1.3.3.14; OpenStax 2.6
g1 above 0	Skewed right	NIST 1.3.5.11
Mean above median	Common in right-skewed data; the mean is pulled toward the tail (“often”, not always)	OpenStax 2.6
Mean largest, mode smallest	The typical ordering OpenStax shows for a distribution skewed right	OpenStax 2.6

Because the median is less affected by the tail than the mean, it is the usual summary to report beside the IQR for data like this. See median and interquartile range for when each is appropriate. The same shape appears as a long upper whisker in a box plot; see how to read a right-skewed box plot.

Assumptions and common mistakes

• Confusing the tail with the peak. A right-skewed histogram looks like it leans left because the bars are tallest on the left. The name follows the tail.
• Relying on one number. NIST calls the histogram “an effective graphical technique” for showing skewness; check the picture and the coefficient together.
• Bin edges change the look. Bin width and which edge each bin includes can alter the shape, especially for small samples. Try more than one width before concluding.
• Assuming mean > median always holds. It is a common pattern, not a guarantee.
• Treating skewed data as normal. Methods that assume a symmetric, bell-shaped distribution may fit poorly. Compare the histogram with a normal curve, as in histograms and the normal distribution, before choosing a test.

How to report it (APA example)

For the example above, one way to write it in APA style is:

Response times were positively skewed (g₁ = 1.68), with a median of 6.5 days (IQR = 5.75) and a mean of 8.9 days (SD = 7.00).

Report the median and IQR alongside the mean when the distribution is clearly skewed, say which skewness formula you used, and include the histogram as a figure. The SD of 7.00 is the usual sample standard deviation (N − 1); the s of 6.82 above is the version the skewness formula uses.

How to calculate and plot it in Excel, R or Python

Excel

=SKEW.P(A2:A21)
=SKEW(A2:A21)
=AVERAGE(A2:A21)
=MEDIAN(A2:A21)

Results for the 20 response times:
SKEW.P = 1.68 (g1, N in the denominator)
SKEW = 1.82 (adjusted sample skewness)
AVERAGE = 8.9
MEDIAN = 6.5

To draw it, select the data and use Insert > Histogram, then set the bin width to 5.

R

y <- c(2,3,3,4,4,5,5,5,6,6,7,7,8,9,10,12,14,17,21,30)
hist(y, breaks = seq(0, 35, by = 5), right = FALSE)
m <- mean(y)
# s uses N in the denominator, as NIST does
s <- sqrt(mean((y - m)^2))
g1 <- mean((y - m)^3) / s^3  # 1.679
c(mean = m, median = median(y), g1 = g1)

right = FALSE makes each bin include its lower edge. For more on drawing histograms in R, see histograms in R.

Python

import numpy as np
from scipy.stats import skew
import matplotlib.pyplot as plt

y = [2,3,3,4,4,5,5,5,6,6,7,7,8,9,10,12,14,17,21,30]
print(np.mean(y), np.median(y))   # 8.9 6.5
print(skew(y))                    # 1.6791 (g1)
print(skew(y, bias=False))        # 1.8184 (adjusted)
plt.hist(y, bins=range(0, 40, 5), edgecolor="black")
plt.show()

FAQ

Is a histogram skewed right the same as positively skewed?

Yes. Both mean the right tail is the long one, and the skewness coefficient is above zero.

Where is the peak in a right-skewed histogram?

Toward the left (the low values). The tail, not the peak, gives the direction its name.

Is the mean greater or less than the median?

Often greater, because the high values pull the mean toward the tail. OpenStax says “often”, so check your own data instead of assuming it.

Which summary should I report?

The median with the IQR describes the centre and spread without being dragged by the tail; the mean and SD can be given as well.

Sources

• NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.11 Measures of Skewness and Kurtosis, itl.nist.gov/div898/handbook/eda/section3/eda35b.htm (checked 2026-10-29).
• NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.3.14 Histogram, itl.nist.gov/div898/handbook/eda/section3/histogra.htm (checked 2026-10-29).
• OpenStax, Introductory Statistics 2e, 2.6 Skewness and the Mean, Median, and Mode, openstax.org (checked 2026-10-29).