Visualizing Methods

Bar Charts for Categorical Variables

Recall the definition of Categorical Variables.

Consider a categorical variable $x$, with sample $\{x_1,x_2,\dots ,x_3\}$, where there are a total of C possible categories for $x$. Assume that the categories are disjoint and exhaustive.

The sample count for category $c$ is the number of observations in $c$:

$$\text{sample count for }c=\sum _{i=1}^{n}1(x_i=c)$$

The sample proportion for categorical variable $x$ associated with category $c$ is the fraction or percentage of observations in $c$:

$$\text{sample proportion for }c=\frac{{\sum }_{i=1}^{n}1(x_i=c)}{n}=\frac{1}{n}\sum _{i=1}^{n}1(x_i=c)$$

Note: The sum of sample proportions is always 1.

Histograms for Discrete and Continuous Variables

Recall the definitions for Discrete Variables and Continuous Variables.

With histograms, we can visualize the sample distribution of variables.

Measures of Location

The sample mean of observations $x_1,x_2,\dots ,x_n$ denoted $\overline{x}$ is given by:

$$\overline{x}=\frac{x_1+x_2+\dots +x_n}{n}=\frac{1}{n}\sum _{i=1}^n{x}_i$$

The sample median of observations $x_1,x_2,\dots ,x_n$ is denoted ${\tilde{x}}_{1/2}$ is the value for which half the observations are below and half are above.