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Descriptive statistics and distributions
Before any statistical test, identify the variable type and the shape of the distribution – they decide which measure of centre and spread fits (mean and standard deviation for a normal distribution, median and interquartile range for a skewed one).
Why it matters in the exam
Items on this topic give a distribution (for example symptom duration that is normally distributed with a mean and a standard deviation) and ask what percentage of patients falls in a certain range, or show a skewed histogram and ask how the mean relates to the median. Other items ask you to identify a variable type – nominal, ordinal, interval or ratio – or to distinguish the standard deviation, which describes the spread of the data, from the standard error, which describes the precision of the estimated mean and shrinks as the sample grows. A recurring point is the 68–95–99.7 rule in a normal distribution, and another is the effect of an outlier: it moves the mean far more than the median. Understanding these differences also lets you choose later between parametric and non-parametric tests, and explain why the median is reported for income, length of stay or time to an event. Another common item gives a mean and standard deviation and asks what percentage of people is expected to lie above a certain value; here you count how many standard deviations separate the value from the mean, and remember that the distribution is symmetric, so half of the remainder lies on each side. Remember too that a standard deviation large relative to the mean, in a variable that cannot be negative, hints at a skewed distribution.
Key points
- The variable type and the shape of the distribution decide the appropriate measures.
- In a normal distribution 68%, 95% and 99.7% of values lie within one, two and three standard deviations.
- With right skew the mean is higher than the median.
- The median and interquartile range are robust to outliers.
- The standard error equals the standard deviation divided by the square root of the sample size.
Summary table
| Concept | What it describes | When used | Exam point |
|---|---|---|---|
| Mean and standard deviation | Centre and spread of symmetric data | A quantitative variable with a normal distribution | An outlier moves the mean |
| Median and interquartile range | The middle value and the middle 50% of the data | A skewed distribution or an ordinal variable | Robust to outliers |
| Mode | The most frequent value | A nominal variable | There can be several modes |
| Normal distribution | A symmetric bell | Height, blood pressure, many laboratory values | 68% within one standard deviation, 95% within two, 99.7% within three |
| Right (positive) skew | A long tail towards high values | Length of stay, income | The mean is higher than the median |
| Standard error | The precision of the estimated mean | Building a confidence interval | The standard deviation divided by the square root of the sample size |
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Sources
- Kirkwood & Sterne, Essential Medical Statistics, 2nd ed., 2003 — Defining the data; Means, standard deviations and standard errors; The normal distribution
- Altman, Practical Statistics for Medical Research, 1991 — Describing data
Sources are given for further reading; the text is written afresh and not copied from them.
Reviewed by the Examqo AI Professor · 2026-11-06. The text may contain errors; when in doubt, check the source.