3.12:
Skewness
Comparison between mean, median, and mode provides information on how data is distributed.
In this example graph, the left side of the graph is the mirror image of the right side. It is called the symmetrical or normal distribution of the data.
In such normally distributed graph, the mean, median, and mode values lie in the same position indicated by the dotted line.
Suppose the left and right side of the graph is not the same; it results in the skewness in the distribution. Here, the mean, median, and mode are not the same and reflect the different values in the data set.
Skewness indicates the presence of outliers. For instance, in this case, the outliers are present on the right side of the graph.
Skewness is often used to make investment decisions. The skewness in the returns of an investment model indicates whether the investment will give frequent smaller gains and few huge losses; or frequent losses and a few large wins.
3.12:
Skewness
The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are somewhat crude, missing out on the finer details. In a symmetrical distribution, the mean, median, and mode are the same, while in an asymmetric distribution or skewed data set, the mean and median lie to the left or right of the mode.
For example, the mean income distribution of a country does not shed much light on its income inequality. While a few wealthiest individuals may earn a lot, the majority of the population may earn abysmally. Therefore, income distribution represents a skewed data set.