P.S. When you are not in a statistics or math class, use the word "average" and use it with the meaning "sum divided by count."

In ordinary non-technical English, only the word "average" is used, and it refers to a calculation consisting of the sum of a set of numbers divided by the count. The average of 50, 60, and 100 is (50 + 60 + 100) / 3 = 210 / 3 = 70. In mathematics and statistics, "mean" is considered to be a better word to use. There are at least three different kinds: the arithmetic mean, the geometric mean, and the harmonic mean. If the kind isn't specified, it means "arithmetic mean" which is the same thing as the ordinary "average." The arithmetic mean is one measure of the center of a cluster of values. It is usually contrasted with the "mode," which is the most commonly occurring value, and the "median," which is the halfway point--half the values in the group lie above it and half lie below it. If there are three people in a room, and one has a net worth of €100,000, one has a net worth of €200,000, and one is Michelle Ferrero with a net worth of €18.5 billion, their median net worth is €200,000 but their mean net worth is €6,166,766,666 In finance, "average" can mean "compound average growth rate" which is actually the geometric mean of the percentage growth of an amount of money. If a mutual fund earned 10% in 2011, 20% in 2012, and 30% in 2013, then the three-year "average" return would be, not 20%, but 19.72%. In ordinary, but somewhat literary English, "mean" can just mean some midway path or course, most commonly in the phrase "golden mean"--the best, moderate, in-between path.

My understanding (as an ordinary person rather than a maths or statistics expert) is that a 'mean' is a type of average. If you want to find out a mean highest temperature for a month for example, in which some days the temperature was around 20 degrees and some days it went up to 30 degrees, you would add up all the temperatures for each of the 30 days in the month (giving you a total of 7500, say), then divide it by 30. This will give you a mean temperature of 25 degrees. Other types of average are the mode and the median.

There are different kinds of averages. The mean is the most common (ex. the mean of 1,4 and 10 is 7.5). There's also the median, which is the number in the middle of a set of numbers in order (ex. the median of 1,2,3,4 and 10000 is 3). The mode is the number that occurs most frequently in a list. (ex. in 1, 1, 2, 5, and 10, the mode is 1 because it occurs once whereas all the other numbers only occur once). All of them can be said to be a measure of average and in mathematics you would have to specify which one you mean. When people say 'average' and don't specify which one they mean, you can assume they're talking about the mean, especially in spoken language.

As far as I know, the most basic difference between them is that the word "average" can be used in everyday situations, whereas "mean" is a mathematical term. By definition, as Wikipedia puts it, "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)." You can say "an average person", but you can't say a "mean person" (well, you can say, but then it MEANs something else). In the sense of "average" in sciences, "mean" is used, e.g. mean value, root mean square, arithmetic mean.