Measures of Central Tendency

There are three main measures of central tendency: mean, median, and mode. Mean is the sum of all data points divided by the number of data points. Median takes the middle point of an ordered data set (or the average of the middle two if there are an even number of data points). Mode is the most common data point.

Continuous Mean Tracking

Say we have already calculated the mean for a set of data. If we get a new data point, is there a way to calculate the new mean without having to replug in past data points? Yes — continuous mean tracking.

Where $m$ is the number of data points including the new value, $x_m$ is the value, and $\mu_m$ is the new mean that has the new value (meaning $\mu_{m-1}$ is the old mean).

\[\mu_m = \mu_{m-1}\cdot\frac{m-1}{m}+\frac{x_m}{m}\]