# Z-Scores (Standard Scores)

In statistics, a normal distribution is also called a Z-distribution or Gaussian distribution. A normal distribution is a range of values that fits a classic bell-shaped curve, with the mean, median and mode all on the centre-line (figure 1). Many natural biological parameters when sampled fall into this bell shaped curve including height, blood pressure, intelligent quotient and weight. In a normal curve, 50 % of the values will be above the mean and 50 % will be below the mean. The standard deviation (σ) is a measure of how spread out the values are and 1 standard deviation represents 68 % of the population (34.13 % each side of the mid line), 2 standard deviations represent 95% of the population (34.13 + 13.59 % × 2) and 3 standard deviations represent 99.7 % (34.13 + 13.59 + 2.14 % × 2) of the population. Standard scores or Z-scores are a way of stating the number of standard deviations that a stated score is above or below the mean value. A Z-score of +3 therefore represents a value 3 standard deviations above the mean, whereas a Z-score of -2 represents a value 2 standard deviations below the mean. Figure 1. A diagrammatic representation to show Z-scores (standard scores) on a normal curve. The mean, median and modal average are all equal to the centre-line on the curve. The z-score value represent the number of standard deviations that a stated score is above (+) or below (-) the mean value. In this case, a z-score of +3 represent 3 standard deviations above the mean (97.5% of the population) and +2 represent 2 standard deviations above the mean (95% of the population).