Limitations of the Measure of Central Tendency Statistics

Statistics have always been a topic of mystery for a lot of individuals, while others have there own bright ideas when it comes to the use of this science.

As we know, the most common statistical parameters are easy to understand and decipher, though there are some nuances that we need to keep in mind while using these parameters. In this article, we will try to understand those nuances and their unknowns by exploring their limitations.

Limitations of the Mean:

1. The mean cannot be calculated for categorical data, as the values cannot be summed.
2. As the mean includes every value in the distribution the mean is influenced by outliers and skewed distributions.

Limitations' Standard Deviations

It gives more weight to extreme items and less to those which are near the mean. It is because of this fact that the squares of the deviations, which are big in size, would be proportionately greater than the squares of those deviations, which are comparatively small. Deviations 2 and 8 are in the ratio of 1:4, but their squares, i.e., 4 and 64, would be in the ratio of 1:16.

Next Logical Question That Comes to Mind Is, What Should We Do?

The answer is simple, use MAD (Median Absolute Deviation). MAD is mostly used to overcome the outlier effect on a sample population. It is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence them. In the MAD, the deviations of a small number of outliers are irrelevant.

What About the Scenarios Where We Need to Understand the Measure of Centrality for Categorical Values?

Go for mode, as mode is nothing but the most frequently occurring value in a particular distribution.

For example, consider the dataset below that shows the retirement age of 11 individuals in a particular year:

54, 54, 54, 56, 56, 58, 57, 58, 59, 60, 54

The most frequently occurring value in the above data set is 54. Therefore, the mode for this dataset with categories (retirement age) is 54.

The above are few examples that will force us to scrutinize the scenarios in which we implement these statistics and ensure that we do not end up making a fatal mistake resulting in "Death by Statistics."