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Average vs Mean vs Median vs Norm vs Par

Average, mean, median, norm, par denote something and usually a number, a quantity, or a condition that represents a middle point between extremes. Of these words average, mean, median, and par are also used as adjectives.

Average is an arithmetical term applied to a quotient obtained by dividing a total by the number of items entering into this total so that the quotient represents the value each item would have if all were alike; thus, the average of 10, 12, 14, 16, 18, 20 is 15 (that is, 90 + 6).

Such averages are computed to give one a fair estimate of a group or a series in which there are inequalities. When (as in sports) the total represents the number of chances taken or of  pportunities offered or provided, the average is obtained by dividing the number of successes or successful performances by this total.

Such an average may be expressed as a percentage or a permillage and gives a fair estimate of a player’s performance and a basis for comparison with others; thus, a baseball first baseman who handles a total of 1114 chances and makes 6 errors has a fielding average of .9946 (that is,’ 1108 -^ 1114); a baseball batter who is credited with 605 appearances at bat and has made 201 hits has a batting average of .332 (that is, 201 -r- 605).

A similar method is used in estimating probabilities (as the chances of death for a person between given ages and the length of the period between recurrences of an unpredictable phenomenon); thus, the average of mortality for persons of a given age is computed from statistics of deaths at that age and of the population group consisting of persons of that age.

Average also may be applied to a concept of what is the typical or ordinary person or thing of its kind (see also average, under MEDIUM).

Mean originally and still in certain idioms named a condition, quality, intensity, or rate that is midway between two extremes <observe a happy mean between abjectness and arrogance or between effusiveness and reserve).

In its mathematical use mean is more general than average (for which another name is arithmetical mean): it covers also the geometric mean, that is, the square root of the product of two numbers or quantities (or the nth root of the product of n quantities); thus, 10 is the arithmetical mean or average of 4 , 16; while 8 is the geometric mean of 4 , 16. Median refers to a midway point in position; in statistics it names the figure or quantity which represents the point at which there are as many instances below as there are above it; thus, the average of a group of 5 workers earning respectively 6, 8, 10, 16, and 20 dollars a day is 12 dollars a day, whereas the median for the same group is 10 dollars, because one half of them earn less than 10 dollars a day and one half more.

Norm suggests a rule for guidance or a definite pattern to be followed; it also denotes especially in such fields as psychology and sociology, an average, whether mathematically computed or estimated, of performance or achievement of a group, class, or category that can be set up as a standard for or a minimum of accomplishment by a similar larger group, class, or category; thus, a course of study for a particular school grade is based upon a norm determined by the performance of children of the age, experience, and background commonly found in that grade.

Par usually refers to an average for an individual that is like the norm for a group. It often refers to an individual person’s average in health, accomplishment, or performance.

In British use par may be employed in reference to an average in amount.