Continuous Data
Continuous data is numerical data that can take any value within a range, limited only by the precision of the instrument measuring it — height, temperature, reaction time, revenue down to the cent. Between any two continuous values there is always, in principle, another possible value, which is the property that separates it from discrete data's countable, gap-filled set of possibilities; a person's height isn't restricted to whole numbers of centimeters, it's restricted only by how precisely it was measured.
This infinite-divisibility property is what makes continuous data the natural fit for probability density, as opposed to the probability mass used for discrete outcomes — and the difference changes what a probability even means for continuous data. For discrete data, a probability distribution assigns an actual probability to each specific value (the probability of exactly 3 defects is a real number you can state). For continuous data, the probability of any single exact value is technically zero — the probability of someone being exactly 170.00000... cm tall, to infinite precision, is vanishingly small — so continuous distributions instead describe the probability of falling within a range, via a probability density function, with the normal distribution the most common example. This is a genuine conceptual shift, not just a technicality, and it's why questions about continuous data get phrased as "what's the probability height falls between 165 and 175 cm" rather than "what's the probability height equals 170 cm."
In practice, continuous data is nearly always recorded at finite precision, which creates a persistent tension between the mathematical idealization (infinitely divisible) and the stored reality (rounded to some number of decimal places), and that gap is where a specific, common measurement problem lives: discretization or binning error. Grouping continuous data into bins for a histogram or a simplified category (age into "18-24," "25-34," etc.) is standard practice for visualization and some modeling approaches, but it necessarily discards information — two ages at opposite ends of the same bin are treated identically — and the choice of bin width can materially change the apparent shape of a distribution, which is why histogram bin width is treated as an analytical decision with real consequences rather than a cosmetic one.
Continuous data supports the full range of classical parametric statistics — means, standard deviations, Pearson correlation, linear regression, t-tests — because these methods were built around the assumption of a continuous, often normally distributed, underlying variable, and their mathematical derivations rely on that continuity. Applying them to data that's actually discrete (especially with a small number of possible values) is a common approximation that's often acceptable in practice but technically imprecise — treating a 5-point Likert scale as continuous enough for a t-test is widespread and usually defensible with a large enough sample, but the underlying statistical machinery was built for data that doesn't have discrete gaps in it.
Measurement error compounds differently for continuous data than for other types: because the "true" value is assumed to exist at infinite precision, every recorded continuous value is implicitly an approximation, and propagating that uncertainty — through confidence intervals, error bars, and formal measurement-error models — is a dedicated subfield of statistics that discrete and categorical data mostly don't need, since a count of 5 customers is exactly 5, with no instrument-precision question attached to it the way a weight of 5.0 kg always has.
Read continuous data as the numerical type defined by infinite divisibility rather than by any specific unit: that single property is what forces probability to be described in ranges rather than exact values, makes binning choices a real analytical decision rather than a formality, and underlies the entire apparatus of classical parametric statistics that assumes, even when the data in front of it is only an imprecise stand-in, that a true continuous value exists underneath.