Quantitative Data
Statistics & ProbabilityQuantitative data consists of numerical values that represent measurable quantities, such as height, weight, or temperature.
Definition
Quantitative data is data made up of numbers that can be measured or counted. It answers questions like "How many?" or "How much?"
Example
The number of books a student reads ($3$, $7$, $12$) and the temperature each day ($72$, $68$, $75$ degrees) are quantitative data.
Key Insight
If you can add, subtract, or average the values meaningfully, it is quantitative data.
Definition
Quantitative data consists of numerical measurements or counts. It is divided into discrete data (countable, e.g., number of siblings) and continuous data (measurable on a continuous scale, e.g., weight). Quantitative data supports arithmetic operations and measures like mean and standard deviation.
Example
Annual salary ($\$47{,}000$; $\$82{,}000$; $\$35{,}500$) is quantitative continuous data. The number of cars owned ($0$, $1$, $2$, $3$) is quantitative discrete data.
Key Insight
The distinction between discrete and continuous matters for modeling: count data often uses Poisson or negative binomial distributions, while continuous measurements often use normal or other continuous distributions.
Definition
Quantitative data takes values in a subset of the real numbers. Continuous quantitative variables are modeled with probability density functions; discrete ones use probability mass functions. Measurement scales (interval vs. ratio) affect permissible operations: ratio scales have a true zero, enabling meaningful ratios.
Example
Temperature in Celsius is interval-scale quantitative data (differences meaningful, no true zero). Mass in kilograms is ratio-scale (true zero exists, so "twice as heavy" is valid). Treating interval data as ratio leads to meaningless comparisons.
Key Insight
Stevens' levels of measurement (nominal, ordinal, interval, ratio) provide a hierarchy that determines which statistical analyses are mathematically valid for a given dataset.