mean

1.

(ethical) In many ethical systems the right path is presented as one that strikes a happy medium. It strays neither one way nor the other, but represents moderation, harmony, balance, and the avoidance of pitfalls on either side. Aristotle's doctrine of the mean represents all virtues as striking a balance between vices of excess and vices of defect. The man who fears everything is a coward, but the man who fears nothing is rash; the man who indulges every pleasure is self-indulgent, but the man who indulges none is a boor. A similar idea was already present in the Philebus of Plato and is derived from Pythagoras . The doctrine is prominent in Confucianism : in the Analects, Confucius writes of the harmonious life as one avoiding excesses and deficiencies, and in which wisdom is gleaned from both old and young, low and high. K’ung Chi, the grandson of Confucius, wrote a work entitled the Chung Yung, or mean of equilibrium and harmony. The anonymous work The Doctrine of the Mean was a basic text for civil service examinations in China from 1313 until 1905. In the Buddhist System of the Middle Way the principle repudiates both exaggerated asceticism and easy-going hedonism. The term ‘golden mean’ is from the Latin poet Horace, whose aurea mediocritas is described in Odes 2. 10. 5.

2.

(mathematical) That which occupies a middle position. In mathematics an arithmetical mean of n quantities is their sum, divided by the number n. The geometrical mean of n quantities is the nth root of their product. The harmonic mean is the reciprocal of the arithmetical mean of their reciprocals. In statistics the mean value of a distribution of a random variable x is a weighted mean of its values, where the weight of a value f(x ) is the probability of the value. The mode of a distribution is the most common value, and the median is the value such that the probabilities of x being less than or greater than this value are each 0.5 (or as near 0.5 as the distribution permits).