What does a histogram with a long left tail indicate?

A histogram with a long left tail indicates a distribution that is negatively skewed or left-skewed.

In a negatively skewed distribution, most of the data points are concentrated on the right side of the histogram, with fewer data points extending towards the left. This creates a "tail" that stretches out to the left. The peak of the histogram, where the highest bars are located, represents the mode, which is the most frequently occurring value in the dataset. In this case, the mode is higher than the median and the mean.

The mean, median, and mode are measures of central tendency that help us understand the centre of the data. In a negatively skewed distribution, the mean is pulled to the left by the lower values in the tail, making it less than the median. The median, which is the middle value when the data is ordered, is also less than the mode. This relationship between the mean, median, and mode is a key characteristic of a negatively skewed distribution.

Negatively skewed distributions can occur in various real-world situations. For example, in a test where most students score high marks but a few score very low, the distribution of scores would be negatively skewed. Understanding the shape of the distribution helps in analysing the data more effectively and making informed decisions based on the data.