Introduction
This topic covers the normal (Gaussian) distribution, the most important continuous probability model in medical statistics. It explains the bell-shaped pattern of many biological measurements, the 3-sigma rule used to judge how unusual a value is, and the central limit theorem, which justifies most inferential methods used later in the course.
Definition and shape of the normal distribution
The normal distribution is a continuous, symmetric distribution described by two parameters: the mean \mu (location) and the standard deviation \sigma (spread). Its density function is given below. The curve is bell-shaped, centred on \mu, and its tails extend indefinitely in both directions but approach zero quickly.
- The mean, median and mode coincide at the centre of the curve.
- The curve is symmetric, so skewness is zero (skewness and kurtosis are covered in topic 21).
- The inflection points lie at \mu\pm\sigma; a larger \sigma gives a flatter, wider curve, while the location of the peak depends only on \mu.
- The total area under the curve equals 1, so areas between two values give probabilities.