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The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.
The median
Yes. In the set (9, 10, 11, 12, 13) 11 is the median and the mean.
The Median is a form of average. Mathematically, the average is the sum of all values, divided by the number of values there are. This is known as the arithmetic mean. An Average is meant to give a representative value of all of your values. If you have a lot of numbers that are very similar and then one that is massively out of proportion with all the others, then the mean doesn't give a representative value. There are also two other forms of average, other than the arithmetic mean. They are the Mode and Median. The Mode is the most common value in a list and the Median is the middle value when all are arranged in numerical order. Sometimes it is better to use them.
The median is the value which seperates the upper and lower half of a set of numbers. The mean is the average value between two or more numbers. In calculating a set of numbers, specifically a set of averages, the median may indeed be effected by the mean.