What does a histogram with a long right tail indicate?

A histogram with a long right tail indicates a positively skewed distribution, where most data points are concentrated on the left.

In a positively skewed distribution, the majority of the data values are clustered towards the lower end of the range, with fewer values stretching out towards the higher end. This creates a "tail" that extends to the right. For example, if you were looking at the distribution of exam scores in a class, a positively skewed histogram might show that most students scored relatively low marks, with only a few students achieving very high scores.

This type of distribution is common in real-world data. For instance, income levels in a population often show positive skewness, where most people earn moderate amounts, but a small number of individuals earn exceptionally high incomes. When you see a histogram with a long right tail, it suggests that there are outliers or extreme values on the higher end of the data set.

Understanding the shape of a distribution is crucial for analysing data because it can affect the measures of central tendency, like the mean and median. In a positively skewed distribution, the mean is usually greater than the median because the high values pull the mean to the right. This can provide insights into the nature of the data and help in making informed decisions based on the analysis.