Descriptive Statistics of a Variable – Roadmap

In Dissecting a Dataset, we showed the elements of a dataset from an eagle’s eye. In the simple dataset we used there, it is easy to examine a variable of the dataset by viewing it in Excel or any spreadsheet software or even a text editor. This is because we had only 12 observations in that dataset and only 2 variables; But what to do when we have thousands (or millions?) of observations? Clearly, viewing the data by visualizing it in a spreadsheet is not a feasible option, as one gets lost in the numbers and detecting a pattern in this case is hard, especially if the data comes from a real life process which turns out to be highly volatile and prone to be affected by many many factors.

Due to what is mentioned above, and also sometimes the need to tell something about your data to someone without giving them all the data, came the need to find a formal and exact way to describe data variables and so, some measures have been defined for this very matter.

First I will give a general idea about the measures of central tendency of a random variable, namely, the mean, median and mode, then I will dedicate a post for each of them in this list:

• Mean (the arithmetic average).
• Median.
• Mode.

Then I will go further to describe the measure of dispersion of a random variable:

• Range and Interquartile Range (IQR).
• Variance.
• Standard Deviation.

Then I will discuss how the measures of central tendency change in relation to each other, and how they affect and are affected by the measures of dispersion. Stay tuned!