The shape of the distribution

The shape of the distribution

The shape of the distribution may be judged by looking at the histogram or by comparing the mean and median.

With symmetric data, the mean and median are theoretically the same although we would consider the distribution to be symmetrical if the mean and median are about the same.

When the data are skewed right (or positively skewed), the mean exceeds the median.

When the data are skewed left (or negatively skewed), the mean is below the median.

The below figure shows the 3 type of the above situations

The below table summarizes the symptoms of skewness in a sample. Because few data sets are exactly symmetric, skewness is a matter of degree. Due to the nature of random sampling, the mean and median may differ, even when a symmetric population is being sampled. Small differences between the mean and median may not indicate significant skewness and may lack practical importance.