Constructing Graphical and Tabular Displays of Data: Dotplots, Stemplots, and Time-Series Plots

Discrete Variable: A variable that contains gaps between successive possible values. For example, the number of times a person has traveled to the Grand Canyon is discrete because it must be a whole number like $0$ , $1$ , $2$ , etc.
Continuous Variable: A variable that can take on any value between two possible values. For example, the amount of time in seconds to run $100$ meters is continuous (e.g., $10.59329$ seconds).

Dotplots: Data points are plotted as dots above a number line. Observations occurring more than once are stacked vertically using equal-sized dots.
Frequency: The number of times a specific observation occurs within a dataset.
Frequency Distribution: A summary of observations paired with their respective frequencies.
Outlier: An observation that is significantly smaller or larger than other observations in the set (e.g., a test score of $38$ points in a group ranging up to $100$ ).

Definition: The $k^{th}$ percentile is a value greater than or equal to approximately $k\%$ of observations and less than approximately $(100 - k)\%$ of observations.
Calculating Percentile of a Score: Found by dividing the number of scores less than or equal to that value by the total number of scores. For example, $8/35 \approx 23\%$ , making the score the $23^{rd}$ percentile.
Finding Value at a Percentile: Multiply the total number of observations by the target percentage and count observations from left to right on a dotplot. For example, to find the $15^{th}$ percentile of $35$ scores: $0.15 \times 35 \approx 5$ , so the $5^{th}$ dot represents the value.

Stem-and-Leaf Plot: A display that breaks data values into two parts: the leaf (the rightmost digit) and the stem (all other digits).
Example: In the value $375$ , the leaf is $5$ and the stem is $37$ .
Construction: Stems are listed in a column from smallest to largest, and leaves are listed horizontally from smallest to largest next to their corresponding stem.

Definition: A coordinate system plot where the horizontal axis represents time and the vertical axis represents another quantity.
Structure: Points are plotted for each time interval and connected by line segments to show trends over time.