STP 231 LECTURE 1: Variables and Data Representation

Flashcards covering definitions, types of variables, graphical displays, grouping methods, and distribution shapes for STP 231.

What is a variable in statistics?

A characteristic of a person or a thing that can be assigned a number or a category.

How are variables and their specific values denoted notationally?

Variables are denoted using capital letters (such as $X$, $Y$, or $Z$), while specific values of a variable are denoted using lower-case letters (such as $x$, $y$, or $z$).

What is the difference between a numeric variable and a categorical variable?

A numeric variable records the amount of something (numerical information), whereas a categorical variable records which of several categories a person or thing is in.

What is an ordinal variable?

A ranked categorical variable.

What is the difference between a discrete variable and a continuous variable?

A discrete variable has a finite number of possible values, whereas a continuous variable has an infinite number of possible values.

What is a frequency distribution?

A listing of distinct values from the data set along with their frequencies (number of occurrences).

How is relative frequency defined?

The ratio of frequency to the total number of observations in the data set.

Why is relative frequency often preferred over simple frequency?

Relative frequency is often preferred when comparing two or more data sets.

What is a bar chart and what type of data is it used for?

A graph drawn using vertical bars where the height of each bar represents the frequency or relative frequency of each category. Bar charts are used for categorical data, and their vertical bars are kept separate.

What is single-value grouping?

A method of grouping quantitative data in which each class represents a single possible value.

What is cutpoint grouping?

A method of grouping quantitative data in which each class consists of a range of values. The smallest value in a given class is the lower limit (lower class cutpoint) and the smallest value that can go in the next higher class is the upper limit (upper class cutpoint).

What is the rule regarding the number of classes in cutpoint grouping?

The number of classes should be between $5$ and $20$.

What is a dotplot?

A graphical display of data using dots, where each dot represents one possible value in the data set.

How is a value split in a stem-and-leaf plot?

Each possible value is split into a stem (the first digit or digits) and a leaf (usually the last digit).

What is the primary disadvantage of dotplots and stem-and-leaf plots?

When the data set is large, dotplots and stem-and-leaf plots will not be informative, making a histogram more useful.

What is a histogram?

A graph drawn using vertical bars where the height of each bar represents the frequency or relative frequency of each possible value or range of values in the data set.

What defines the distribution of a data set?

A table, graph, or formula that provides all values in the data set and how often they occur.

How are unimodal, bimodal, and multimodal distributions defined?

A unimodal distribution has one peak, a bimodal distribution has two peaks, and a multimodal distribution has two or more peaks.

What is a symmetric distribution?

A distribution whose graph can be divided into two parts that are mirror images of each other.

What is the difference between a left skewed and a right skewed distribution?

A left skewed distribution has a longer left tail, whereas a right skewed distribution has a longer right tail.

What type of distribution modality is represented in this graph?

Unimodal distribution

What type of distribution modality is represented in this graph?

Bimodal distribution

What distribution shape is shown in this graph?

Left skewed distribution

What distribution shape is shown in this graph?

Symmetric distribution

What distribution shape is shown in this graph?

Right skewed distribution