Data Distributions and Measurement Levels

A measurable or observable source of data that can change between observations (e.g., temperature, height, brand of car).

Data points represented by numbers, which can be further classified as discrete or continuous.

Data points represented by words or labels, which can be further classified as ordinal or nominal.

Data points that are distinct and separate, with defined gaps between them. Often collected by counting. (e.g., number of goals scored).

Data points that can occur anywhere along a continuum, with no gaps between possible values. Usually collected by measurement. (e.g., height, temperature).

Discrete data involves distinct, separate data points with gaps between them, usually collected by counting, while continuous data allows for any value within a range, often collected through measurement.

Examples include the number of goals scored in a game, the number of children in a family, or the number of products sold daily.

Examples include the height of a person, the temperature of a room, or the length of a piece of fabric.

Data that can take any value within a range. It is measured and can be infinitely divided, meaning there are potentially an unlimited number of values between two data points.

Data that can only take specific, separate values. It is counted and is typically whole numbers.

Categorical data that has a natural order or ranking. The categories can be arranged from least to greatest or vice versa.

Categorical data that does not have a natural order or ranking. The categories are simply different names or labels.

Examples include height, weight, temperature, time, and distance. These can take any value within a meaningful range.

Examples include the number of students in a class, the number of cars in a parking lot, or the number of goals scored in a soccer game. These can only take specific, separate values.

Examples include product ratings (e.g., good, better, best), customer satisfaction surveys (e.g., very satisfied, satisfied, neutral), or exam grades (A, B, C, D, F).

Examples include hair color, favorite animal, gender, or type of car. These categories are simply different names or labels, with no inherent order.

A system for classifying data based on the properties of the data and what kinds of statistical analysis can be applied meaningfully.

The simplest level of measurement. It categorizes data into groups with no inherent order.

Data can be ordered or ranked, but the difference between categories may not be equal.

Data can be ordered, and the differences between categories are assumed to be equal, but there is no true zero.

The highest level of measurement. Data can be ordered, the differences between categories are equal, and there is a true zero point, meaning the absence of the quantity being measured.

The key difference is the presence of a true zero. Interval scales have no true zero point, while ratio scales do.

Ratio scale, as it has a true zero point (0 people means no population) and the difference between population sizes is meaningful (we can compare the ratio of populations).