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Why do we use mean rather than average?
Why is mean more commonly used than average?
Why do we use mean instead of average?
Is different using both terms colloquially vs using them in an academic setting?
Mean versus average
- The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without qualification, I think most people would assume that "mean" refers to the arithmetic mean.
- Average has many meanings, some of which are much less mathematical than the term "mean". Even within the context of numerical summaries, "average" can refer to a broad range of measures of central tendency.
- Thus, the arithmetic mean is one type of average. Arguably, when used without qualification the average of a numeric variable often is meant to refer to the arithmetic mean.
Side point
- It is interesting to observe that Excel uses the sloppier but more accessible name of
AVERAGE()for its arithmetic mean function, where R usesmean().
There are several "averages." Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or "arithmetic average" is one average that you learned in the past. But the median (the value with half the observations greater and half less than it), the mode (the most common value), the geometric mean (multiply the values then take the nth root), the harmonic mean (the reciprocal of the mean of the reciprocals of the data), and others all fall under the general term "average."
People looking for this question might find the following helpful:
In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable
, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value
of
and its probability
, and then adding all these products together, giving
.
Source: Wikpedia
In colloquial language average usually refers to the sum of a list of numbers divided by the size of the list, in other words the arithmetic mean. However, the word "average" can be used to refer to the median, the mode, or some other central or typical value. In statistics, these are all known as measures of central tendency. Thus the concept of an average can be extended in various ways in mathematics, but in those contexts it is usually referred to as a mean (for example the mean of a function).
Source: Wikpedia
In statistics and probability theory, the median is the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.
Source: Wikipedia
One guy gives you 2 dollars.
Second guy gives you 7 dollars.
Third guy gives you 3 dollars.
One guy gives your friend 4 dollars.
Second guy gives your friend 4 dollars.
Third guy gives your friend 4 dollars.
You both got 12 dollars. On average, you both got 4 dollars per person. He also actually got 4 dollars 3 times, so his average is easy to see is 4. You got different amounts of money, so your average has to be found as 12/3.