The weight rounding trap
You’re discussing a patient’s ICU length of stay over rounds. The chart says “14.3 days.” Your colleague says “So about two weeks, right?” Another nods: “Yeah, 14 days flat.”
Two weeks, 14.3 days, or 344 hours — those are three different numbers. Which one do you use to judge whether the new early‑mobility protocol really shortened ICU stay?
That question highlights why the type of data you have matters. The statistic you report, the plot you draw, and the test you run all hinge on whether the underlying measurement is categorical, continuous, or somewhere in between.
If you treat ordinal data as continuous (e.g., assigning 1, 2, 3, 4 to pain scores and averaging them), you risk a meaningless mean. If you treat continuous data as categorical (e.g., splitting age into “young/middle/old” without preserving the scale), you lose power.
In this chapter we will walk through the three data families you will see in ICU papers, how to summarise each, and the appraisal checks that keep you from being misled by a poorly chosen summary.
Three families of data
Data type | What it measures | Typical ICU example | The “golden rule” for summarising |
Continuous | A quantitative scale with meaningful intervals; arithmetic operations (add, subtract, average) make sense. | Systolic BP (mmHg), SOFA score, lactate (mmol/L), weight (kg), PaO₂/FiO₂ ratio | Use mean (SD) if the distribution is roughly symmetric and free of extreme outliers; otherwise use median (IQR). |
Discrete / count | Counts of events; the variable can only take integer values. | Number of ventilator‑associated pneumonia episodes, urine output (mL/hr), central line insertions, 28‑day death count (0, 1, 2, …) | Use proportion (events / total) or rate (events / person‑time). The mean of counts is valid but often less informative than a rate. |
Ordinal / ranked | Values have a meaningful order, but the intervals between adjacent values are not assumed equal. | Pain score 0‑10, Richmond Agitation‑Sedation Scale (RASS), Glasgow Coma Scale, SOFA organ-failure sub‑items staged 0‑4 | Use median (IQR) or proportions at each category; avoid reporting a single mean unless you have validated that the intervals are truly equal. |
Why the distinction matters
- Mean ± SD assumes a normal (Gaussian) distribution. If the data are skewed (e.g., length of stay, which often has a long right tail), the mean can be pulled far from the “typical” value by a few extremely long stays. The median is robust.
- Median (IQR) tells you the 50th percentile and the spread of the middle 50% of data. It does not assume symmetry.
- Proportion is for binary outcomes (alive/dead, VAP yes/no). The denominator must be clearly defined (e.g., “proportion of ventilated patients who developed VAP”).
- Rate is for events occurring over time or across a population at risk (e.g., “3 VAP events per 1,000 ventilator‑days”).
In ICU papers, you will frequently see “mean ± SD” reported for variables that are clearly skewed (e.g., “SOFA score 8.2 ± 5.1”). That is a cue to read the full distribution or ask for the median.
Summarising continuous data: mean vs median
When the mean is appropriate
If the variable is approximately normally distributed — symmetric around a centre, with the mean, median, and mode all near the same value — the mean (±SD) is a concise and efficient summary. Examples:
- Systolic BP in a stable cohort of normotensive ICU patients.
- Arterial blood gas pH in a controlled ventilated population.
- Serial lactate measurements in a protocolised early‑clearance bundle.
A quick visual check: a histogram or a boxplot that looks bell‑shaped. If the whiskers in a boxplot are roughly equal and the median line sits in the centre of the box, the mean is likely appropriate.
When the median is appropriate
If the data are skewed, have extreme outliers, or are bounded at zero with a long tail, the median (±IQR) is the safer summary. ICU examples:
- ICU length of stay (often median 3 days, IQR 2–5, mean 7.4 due to a few months‑long stays).
- Ventilator‑free days (censored at 28; typically median 20, IQR 15–23).
- Cumulative fluid balance (positive balances can be huge; median 0, IQR −500 to +800).
In these cases, the mean overestimates the “typical” patient’s experience because a small number of very long stays or large fluid loads pull it up. The median tells you what the typical patient experienced.
Quick appraisal checklist for continuous summaries
When you read a paper and see “mean ± SD” or “median (IQR)”:
- Check the distribution — Does the paper present a histogram, boxplot, or at least report skewness? If not, treat the summary with caution.
- Compare mean and median — If they differ by more than ~20–30%, the distribution is likely skewed, and the median may be more representative.
- Note the sample size — Small n can make the mean unstable; large n can make even a skewed mean informative (because the CLT kicks in), but the median still tells you about the typical patient.
Summarising discrete / count data
Proportions
Binary outcomes are the most common discrete summary in ICU literature: “30‑day mortality 22%,” “VAP rate 15%.” The denominator must always be explicit: “22% of enrolled patients” vs “22% of survivors at 48 h.”
Appraisal check: Verify that the denominator matches the population you think it does. A paper may report “VAP occurred in 12% of patients” without stating that only ventilated patients were at risk — a subtle denominator trap.
Rates
When the outcome can recur or occurs over time, a rate is more informative than a simple proportion. Example: “4 VAP events per 1,000 ventilator‑days.” This accounts for the fact that some patients spend 30 ventilator‑days and others only 2.
Appraisal check: Look for the person‑time denominator. If the paper says “0.5 events per patient‑day” but doesn’t explain whether “patient‑day” includes days extubated, the rate is ambiguous.
Summarising ordinal data
The pain‑score pitfall
A common ICU paper reports: “Mean pain score 3.2 (SD 2.1) on a 0‑10 NRS.” The problem: a 0‑10 numeric rating scale is ordinal, not truly continuous. The distance between 2 and 3 may not be the same as between 7 and 8 for every patient. Averaging across patients assumes equal intervals, which is often unjustified.
What to do instead: Report the median and IQR, or present a bar chart of the distribution (e.g., “40% reported no pain, 35% mild, 20% moderate, 5% severe”).
The SOFA score
SOFA is often treated as continuous (mean 8.2), but each organ sub‑item is ordinal (0‑4). The total SOFA is a sum of six ordinal items; it can be approximately normal in large samples, but the assumption should be checked.
Appraisal checklist for ordinal summaries:
- Does the paper acknowledge the ordinal nature, or does it treat the variable as continuous without comment?
- If a mean is reported, does the distribution look approximately symmetric (via a boxplot or reported skewness)?
- Would a median/IQR or category counts better represent the data?
A unified appraisal checklist for any descriptive statistics table
When you open a methods or results table, run through these four questions:
# | Question | Why it matters |
1 | What data type is being summarised? (Continuous, discrete, count, ordinal) | Determines which statistics are valid. |
2 | Is the chosen summary appropriate for the data type? (Mean/SD for symmetric continuous; Median/IQR for skewed/ordinal; Proportion for binary) | Prevents misinterpretation from mismatched summaries. |
3 | Is the distribution shape reported? (Histogram, boxplot, skewness, or at least mean vs median comparison) | Allows you to judge whether the summary captures the typical value. |
4 | Is the denominator clearly defined? (For proportions/rates: what population? what follow‑up time?) | Avoids denominator‑bias where the number looks meaningful but is based on a different group. |
Go deeper
- StatPearls – “Descriptive Statistics” (NBK430685): free, covers mean, median, mode, SD, IQR, when to use each, with ICU‑relevant examples. https://www.ncbi.nlm.nih.gov/books/NBK430685/
- OpenIntro Statistics – Chapter 2 (Descriptive Statistics) (free PDF): clear explanations of mean/median/IQR with visual examples; includes R code for quick plots. https://openintro.org/stat/textbook.php
- BMJ Statistics Notes – “Presenting data” (Altman & Bland): short, practical guidance on choosing summaries that match data type. https://www.bmj.com/content/bmj_stats_notes
Next: Chapter 6 — Probability foundations: normal, binomial, Poisson