Descriptive Statistics

Descriptive statistics summarize a data set with a few well-chosen numbers and pictures so that its shape, center, and spread become clear at a glance. In IB Mathematics: Analysis & Approaches you work with both raw data and grouped data, and you must be fluent moving between the two.

Measures of central tendency describe a typical value. The mean $\bar{x}$ is the sum of the values divided by how many there are, $\bar{x} = \dfrac{\sum x}{n}$. For data organized in a frequency table with values $x_i$ and frequencies $f_i$, the mean becomes the weighted average $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}$. The median is the middle value once the data are placed in order; for $n$ values its position is the $\left(\frac{n+1}{2}\right)$th data point. The mode is the most frequent value, and for g