Positively Skewed — Definition, Formula & Examples
Positively skewed data is a single-variable distribution where most values cluster at the low end and a few unusually large values stretch out a long tail to the right. It is also called right skewed or positive skew.
A distribution is positively skewed when its right tail (toward larger values) is longer or more drawn out than its left tail, so the bulk of the observations sits at lower values. In such distributions the mean typically exceeds the median, and the moment coefficient of skewness is usually positive. Neither is a guaranteed property. The shape of the graph defines the skew, not these numbers.
Worked Example
Problem: Seven students record their commute times in minutes: 12, 45, 10, 14, 18, 12, 15. Use the median, the mean, and the spread on each side of the median to describe the shape of the data.
Step 1: Order the values. With 7 values, the median is the 4th one.
Step 2: Add the values and divide by 7 to find the mean.
Step 3: Compare how far the data reaches on each side of the median. The right side stretches much farther, and the single large value 45 pulls the mean above the median.
Answer: The right tail reaches 31 minutes past the median, while the left tail reaches only 4 minutes below it. The mean (18) is greater than the median (14). The commute times are positively (right) skewed.
Why It Matters
On the AP Statistics exam, you are expected to describe a distribution's shape and then choose fitting summaries. For right-skewed data such as household income, home prices, or wait times, the median and IQR describe a typical value better than the mean and standard deviation. Those large tail values inflate the mean and the standard deviation.
Common Mistakes
Mistake: Calling a distribution right skewed because its peak (the tallest bar) is on the right side of the graph.
Correction: The skew is named for the tail, not the peak. In positively skewed data the peak sits on the left and the long, thin tail points right, toward larger values.