What is the statistical difference between a mean and a median?

Answer 1

Mean and median are two of the measures of central tendency. They are numbers that give you information about a group of scores. This is important, because you can't very well go around reciting all the scores of a given sample whenever you need to look at or use the sample. The mean is another term for simple average. You add up all the individual scores, and then divide the sum by the number of scores. If your scores are:
1, 2, 3, 6, 8, 14, and 90 then you take their sum, 124, and divide it by 7, the number of scores. You get 17.71, the mean. The mean takes into account the value of every single score. This means that the value of every single score "pulls" the mean toward itself. If any value changes, the mean changes. The median is the score that divides the collection of scores in such a way that half the scores are smaller, and half the scores are larger. Using the same scores above, (they have to be in order) you see that 6, the middle score, divides the group of scores in this way. Three scores are lower, and three are higher. So 6 is the median score. When you have an even number of scores, go half-way between the two middle-most scores. You can see that you could change the actual values of the scores in any number of ways, and still have the same median. This may seem odd, but there may be times when you want your 'estimate' of the population value to be "higher than correct" no more often than it is "lower than correct".