A negatively skewed distribution is one where the long tail extends to the left, toward smaller values, while most data points cluster toward the right, near larger values. It’s also called a “left-skewed” distribution. If you’re looking at a histogram, the peak sits toward the right side of the graph, and the data trails off gradually to the left.
What Makes a Distribution Negatively Skewed
In a perfectly symmetric distribution (like the classic bell curve), data falls evenly on both sides of the center. In a negatively skewed distribution, that symmetry breaks. The bulk of observations pile up at the higher end, but a smaller number of unusually low values drag the tail out to the left. The skewness coefficient, a numerical measure of this asymmetry, is below zero for any left-skewed dataset. A perfectly symmetric distribution has a skewness of zero.
Think of it this way: the tail points in the direction of the outliers. In a negatively skewed distribution, the outliers are the unusually small values, so the tail points left.
How Mean, Median, and Mode Line Up
One of the most reliable ways to identify negative skewness is the relationship between the three measures of central tendency. In a negatively skewed distribution, the mean is less than the median, which is less than the mode. The mean gets pulled furthest to the left because it’s sensitive to those extreme low values in the tail. The median, which simply marks the middle observation, resists that pull. The mode sits at the peak, which is the rightmost of the three.
As a concrete example: if a dataset has a mode of 7, a median of 6.5, and a mean of 6.3, the ordering (mean < median < mode) signals left skew. This ordering reverses in a positively skewed distribution, where the mean is the largest of the three because the tail stretches to the right instead.
Real-World Examples
Age at Death
The distribution of age at death in most populations is negatively skewed. The majority of people live into their 70s and 80s, creating a cluster of values at the higher end. Fewer people die at very young ages, but those early deaths form the long left tail. The peak is near the upper range of the lifespan, with a gradual trail of lower values stretching downward.
Easy Exam Scores
When a test is easy, most students score high, bunching near the top of the scale. A smaller number of students score poorly, producing a left tail. Research published in Educational and Psychological Measurement confirmed this pattern: when the average score on a test exceeds 50% of the maximum possible score, the distribution of results tends to be negatively skewed. The easier the test, the stronger the skew. This can be demonstrated mathematically using a binomial model, where any item that more than half of students answer correctly contributes to negative skewness in the overall score distribution.
Other Common Examples
- Retirement age: Most people retire in a narrow window around their mid-60s, but some retire much earlier due to disability or financial independence, creating a left tail.
- Satisfaction surveys: On rating scales, responses often cluster at the positive end (4s and 5s out of 5), with a thin tail of very low ratings pulling left.
How to Read It on a Graph
On a histogram or frequency curve, a negatively skewed distribution has its tallest bars (or its peak) shifted toward the right side of the horizontal axis. The bars then taper off more gradually to the left. Compare this to a positively skewed distribution, where the peak sits to the left and the tail stretches right toward larger values. The key visual cue is always the direction of the longer tail, not the location of the peak. The tail tells you the type of skew.
A common mistake is confusing the direction of the peak with the direction of the skew. If the peak is on the right, it might feel like “right skew,” but the skew is actually named for the tail direction. Peak on the right, tail on the left: that’s negative (left) skew.
Negative Skew vs. Positive Skew
The simplest way to keep these straight is to remember that the skewness label follows the tail. A negatively skewed distribution has its tail pointing toward negative (smaller) values on the number line. A positively skewed distribution has its tail pointing toward positive (larger) values. Income distribution is the textbook example of positive skew: most people earn moderate amounts, while a small number of very high earners stretch the tail far to the right. Age at death is the mirror image, with the tail stretching left.
In terms of central tendency, the two types are opposites. Positive skew pulls the mean above the median. Negative skew pulls the mean below the median. In both cases, the mean chases the tail because it’s the measure most affected by extreme values.