What is a measure of central tendency ?
Simply put, it is a value that tries to summarize a given dataset. It does so by providing a central (or middle) value that (sort of) represents the entire dataset.
Imagine the marks scored by 10 students in an examination were as follows:
20 20 20 20 20 20 20 20 20 20
If I asked you about the performance of the students, you could say that “student 1 scored 20 marks; student 2 scored 20 marks;……. student 10 scored 20 marks”. The problem with this strategy is encountered when we have to deal with large datasets, of say, 100 values or more. It would take considerable time and effort to describe the entire dataset.
Therefore, people tried to find a way by which they could convey the essence of the dataset.
The measures of central tendency do just that.
It is like describing a person in one word- “smart”/ “creative”, etc. In fact, we summarize things on a routine basis, often without realizing it, whether it be movies, books, classes, or just about anything.
Coming back to the example, one could simply say “the students scored 20 marks on average”.
This average value represents the entire dataset, and gives us an idea about the performance of the students.
Measures of Central Tendency are mathematical ways of summarizing numerical data into (a) single central value(s) that represent the entire dataset.