Statistics and Probability - Data presentation

Data can be classified as Qualitative (categorical) or Quantitative (numerical). Quantitative data is further divided into Discrete (countable values) and Continuous (measurable values, e.g., $h \in \mathbb{R}$).

Grouped Frequency Tables are used for large datasets. For calculations like the mean, the mid-interval value $x$ is used: $x = \frac{\text{lower limit} + \text{upper limit}}{2}$.

Cumulative Frequency is the running total of frequencies. A cumulative frequency graph (ogive) is used to estimate the median ($50^{th}$ percentile) and quartiles ($25^{th}$ and $75^{th}$ percentiles).

Box-and-whisker plots represent the five-number summary: minimum value, lower quartile ($Q_1$), median ($Q_2$), upper quartile ($Q_3$), and maximum value.

Outliers are extreme values that are numerically distant from the rest of the data. The standard IB AI criteria involves the Interquartile Range ($IQR$).

Histograms are used for continuous data. The area of the bar represents the frequency. In most IB AI SL contexts, class widths are equal, so the height of the bar represents the frequency.