2: Centers and Spread

2.2 Some Properties of Centers

Read the textbook

Key Idea 1: Some Properties of Centers...

Discussion

When a data set is roughly symmetric about its center and also has no unusually large or small "extreme" values, the mean is the usual choice to describe its center.
When we want the measure of center that we use not to be overly influenced by a single extreme value, we sometimes choose the median because it is so robust against this unwanted influence.

Example

Key Idea 2: Recovery of the Sum of the Data...

Discussion

It is sometimes important to regain information that may not have been given in a statistical summary of the data.
The median does not enable us to compute the sum of the data, while Mean does.

Illustration

Key Idea 3: Robustness...

Discussion

A statistic (or a statistical method) is robust if It still works, even if the data are not distributed in the way you assume.
The median is robust in the sense that it is not influenced much by a large change in a single data point in the data set.

Exercises

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