What does a skewed histogram tell you about the data?

A skewed histogram indicates that the data is not symmetrically distributed around the mean.

When a histogram is skewed, it means that the data values are not evenly spread out on both sides of the central value. There are two types of skewness: positive (or right) skew and negative (or left) skew. In a positively skewed histogram, the tail on the right side of the distribution is longer or fatter than the left side. This suggests that there are a few unusually high values pulling the mean to the right. Conversely, in a negatively skewed histogram, the tail on the left side is longer or fatter, indicating a few unusually low values pulling the mean to the left.

Understanding skewness is important because it affects measures of central tendency like the mean, median, and mode. In a positively skewed distribution, the mean is typically greater than the median, which is greater than the mode. In a negatively skewed distribution, the mean is usually less than the median, which is less than the mode. This can help you understand the general shape and spread of your data, and it can also inform decisions about which statistical methods to use for further analysis.

For example, if you are dealing with a positively skewed dataset, you might prefer to use the median as a measure of central tendency because it is less affected by extreme values than the mean. Recognising skewness can also help you identify potential outliers or anomalies in your data, which might require further investigation.