What Are the Mean, the Median, and the Mode?
Among the various statistical varieties of averages, know the distinction between the three most common: the mean, the median, and the mode. Writers and editors don’t necessarily have to be working in the realms of science or mathematics to be confronted with one or more of these terms, so it’s best to be familiar with each one and how it differs from the others.
The mean is the type of average most people are used to. To find the mean for a set of numbers, add the numbers together and divide by the number of numbers in the set. For example, if you roll two dice thirteen times and get 9, 4, 7, 6, 11, 9, 10, 7, 9, 7, 11, 5, and 4, add the numbers to produce a sum of 99. Divide that number by 13 to get 7.6 (rounded off to one decimal point), the mean of that set of numbers.
To find the median, sort the numbers by value (4, 4, 5, and so on); the median is the middle number (here, seventh out of thirteen), or 7. The mode is the number that appears most often — in this case, a tie for 7 and 9 (easier to find once you’ve sorted the numbers).
Another factor is the range, the distance between the smallest and largest numbers. Based on the results for the mean, the median, and the mode of the number set above, you can guess the number before you figure it. You’re right: 11 minus 4 equals 7. Every solution in the four operations I just did came out to 7 or thereabouts — though 9 tied with 7 as the mode).
This shouldn’t be surprising: Because I used the roll of two dice to come up with the numbers in the set, the range was fairly tight (12 minus 2 equals 10), so the chances of hitting the same number for the mean, the median, and the range were high. A larger possible range, and a larger set of numbers, would increase the chances of producing different figures.
For that reason, too, none of the resulting values for the mean, the median, the mode, or the range need to correspond to any of the numbers in the set.
As a side note, accept the incontrovertible fact that no matter how many times you roll two dice, your chances of getting a certain number never change: Just as a coin toss is always a 50-50 proposition, you always have a 1-in-11 chance of getting snake eyes, a 1-in-11 chance of rolling a lucky 7, and so on. But try telling a gambler that.
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