Imagine you had a limited bandwidth channel to communicate information about your data to the world. If can make one statement about the data, what would it be? What if you can make two? three? and so on until you can describe your data with the finest granularity and transmit it as through the channel.
This is not an unusual setup, as humans we have a limited reception bandwidth. Suppose I share the following high fidelity description of the sequence of all SAT scores of students that applied to a small college this year.
Your ability to infer any meaningful observations from this sequence is quite limited. You may also find it difficult to say much about this sequence in comparison to another sequence of SAT scores perhaps from the previous year.
4.1 One Descriptive Sentence
If we had one sentence to make, it is natural to think of a statistic to describe the data with. Which of the following would you choose?
The lowest SAT score is 886
The highest SAT score is 1466
The most frequent SAT score is 1279
The median SAT score is 1204
The mean SAT score is 1202.23
Each of these statistics conveys one aspect of the data.