# Central Tendency

Suppose that we have a dataset of housing prices for a certain area:

499 | 525 | 555 |

489 | 475 | 400 |

560 | 571 | 465 |

552 | 535 | 527 |

520 | 562 | 605 |

575 | 550 | 590 |

(All prices are in thousands of US dollars.)

Suppose further that we'd like to come up with a single number that summarizes the data in this dataset. How do we proceed?

Before we answer that question, let's think of some numbers that are definitely *not* reasonable
choices. We can see that with a single exception, all of the prices are in the $400K or $500K range. The single
exception is $605K. So $350K would be too low, and $1.8M would be much too high. We'd probably expect the number
to be somewhere in the $500K range, just looking at the data.

Intuitively, we have a range of values, and we can think of this range in a geometric way, as numbers on a number line. Like this:

This visualization helps us see the way the housing prices are distributed across the range. To choose a single number to represent this set, it would be most reasonable to choose the "center" of this dataset in some sense. But where exactly is that center?

One *(wrong)* way to calculate the center would be to take the midpoint between the top and the
bottom of the range. The top of the range is $605K and the bottom of the range is $400K. This approach puts the
midpoint at $502.5K:

Looking at the number line, though, this proposed center seems problematic. Most of the prices are higher than the midpoint. So while this isn't a horrible first attempt, it does seem a bit too low to be a good summary of the dataset. Part of the problem is that the only data points we've accounted for are the endpoints of the range. A better measure probably incorporates all data points, at least for numerical data.

As it happens, there are multiple common approaches to defining the "center" or "location" of a dataset. In the next few sections, we'll explore these different approaches to measuring central tendency.

## Exercises

**Exercise 1.** Before proceeding further in the course, see if you can think of other ways we
might measure central tendency. (You'll have a chance to see if you were right in the following sections.)