Variables and types of data

A discrete variable is not defined by the fact that its recorded values happen to look like whole numbers. It is defined by the way the quantity arises: it is produced by tallying separate, indivisible occurrences or objects. Admissions, tablets and infections all arise from counting events, so the only admissible answers form a list of isolated steps — 0, 1, 2, 3 — with nothing whatever in between. There can be no such thing as half an admission, because the event either occurred or it did not; the constraint belongs to the phenomenon, not to the pen. A continuous variable arises instead from an act of measurement, and measurement always compares a quantity against the subdivisions of a chosen instrument. Between any two readings there lies a further possible reading, however fine the subdivision becomes, which is why weight, height, temperature and glucose remain continuous even when a particular entry carries no decimal point. The practical test is therefore not what the paper displays but what the number tallies: ask whether the entry was produced by tallying distinct occurrences or by reading a graduated scale. The distinction has consequences when a learner mishandles it. A count cannot be halved and still describe anything, yet totals of counts may be added across patients and divided by the number of patients; the resulting 2.4 admissions per patient is a legitimate average even though no individual had 2.4 admissions. A measured quantity behaves differently: differences between its readings are themselves meaningful, so a drop from 39.2 °C to 37.9 °C is a 1.3 °C fall on any ward. Mixing the two — averaging a count as though it were a smooth measurement, or treating a measured value as a tally of events — yields summaries that no longer describe any real patient.

Every instrument has a resolution, the smallest change it can display, and that limit explains why clinical values are written with a fixed number of decimals. A glass thermometer calibrated in tenths reports 38.4 °C, but the liquid in its column occupies a band rather than a mathematical point, so the reading stands for an interval — roughly 38.35 °C to 38.45 °C. A capillary glucometer working in tenths of mmol/L behaves the same way, and a weighing scale marked in 0.5 kg states an interval whenever it displays 70 kg. Resolution is not the same as accuracy: a device may be fine-grained and still misread, and a well-calibrated device may be coarse. What matters for classification is that the underlying quantity is capable of intermediate values; the display merely truncates them. This is why rounding a value never changes its type. Temperature displayed as 39.0 °C, glucose displayed as 6 mmol/L and weight displayed as 70 kg are all continuous, because each could have taken neighbouring values that the instrument chose not to show. Precision matters for a different reason: it limits what a difference can mean. Two temperatures of 37.1 °C and 37.2 °C differ by one gradation, which is within the uncertainty of a tenth-reading thermometer, so a nurse should not report a definite rise on that evidence alone. Recording a value with more decimals than the instrument supports is equally misleading — 7.82 mmol/L implies a resolution the glucometer does not have, and a colleague reading it will over-trust the figure. The safe habit is to write the value at the resolution of the instrument, keep the unit beside it, and remember that a round-looking entry is still a window on a continuous scale.

The four-way split taught here is not a preliminary exercise that can be forgotten once the figures are collected; it dictates which analyses are legitimate downstream. A qualitative variable supports counting, proportions and cross-tabulation, and it is displayed as a bar or pie chart; computing a mean on it produces a meaningless number. A discrete variable supports totals, frequencies and, when its range is wide, an average count, and it is often displayed as a bar chart with a separate bar for each whole value. A continuous variable is the only kind that supports a meaningful difference between two readings, and it is summarised by an average and a measure of spread and displayed as a histogram or a line graph over time. The reasoning runs in one direction: choosing the wrong summary corrupts everything built on it. A ward that collapses a continuous glucose reading into “high or low” turns a quantity into a category and loses the size of the change; a ward that reports a mean from codes turns a category into a quantity and invents a value no patient has. Both errors survive into audit, quality indicators and published reports, where they are far harder to unpick. Nursing application makes the stakes concrete. If a quality audit asks whether a new admission protocol reduced readmissions, the number of readmissions is a count and the length of stay is a measured duration; the first is compared as frequencies, the second by average duration and spread. Deciding the type before collecting the data also fixes what must be recorded — a category needs a code list, a count needs an unambiguous definition of the event, and a measurement needs its unit and the resolution of the instrument. Getting that decision right at the start costs a minute and saves the whole analysis.