What's the Difference between Mean, Median, and Mode?

Barry Lenson

Okay math students, here’s a head-scratcher for you. What is the difference between the mean, the median and the mode?

StraighterLine has created a terrific video that explains it all.  It’s one of a growing number of instructional math videos that StraighterLine has posted on YouTube. But if you’d rather read about means, medians and modes just now, here’s an explanation.

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Means, Medians and Modes

All three are referred to as measures of central tendency.  That’s another way of saying that they indicate central tendencies that are present within a set of numbers. (In order to determine mean, median or mode, you need a set of numbers, like 12, 8, 7, 15, and 7. Those numbers could represent the lengths of fish you just caught, the number of parking spaces on five different streets – just about anything.)

Okay, here we go . . .

  • The Mean – To arrive at the mean of a set of numbers, you add the numbers up and then divide the sum by the number of numbers you were dealing with.  (This is just like calculating what is called the “average.”)  If your number set is 12, 8, 7, 15, and 7, for example, you would first add all those numbers together (equaling 49) and divide that sum by the number of numbers in your set (5). The result is 9.8. That’s your mean!
  • The Median – This is the “middle” number in the set of numbers that you are dealing with. Think of it this way. Half of the numbers in the set are bigger than the median; half of the numbers are smaller. So to arrive at the median, simply put all the numbers in ascending order, with the smallest first. The number that is smack dab in the middle is the median. Aha you say, what if you have an even number of numbers in your set, not an odd number, so two numbers are in the middle? Well, the solution to that problem is easy; if that is the case, the median is midway between the two numbers that are in the middle of the set. So if your two middle two numbers are 7 and 9, your median is 8 (halfway in between).
  • The Mode – Okay, this is pretty simple. The mode is the number in a set that appears most frequently.  If you are dealing with those numbers we cited at the outset - 12, 8, 7, 15, and 7 – the mode is 7, because 7 appears twice, more than any other number. What if you have a set of numbers in which every number appears just once? Simple! You then have a set of numbers that doesn’t have a mode.

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Putting It All Together

That’s really all you need to know. But here’s an extra credit question for you. Can you use the words mean, median and mode in one sentence? Like these . . .

  • “The officer made a mean face at me, which made me drive over the median, which was not my usual mode of driving.”
  • “The median number of women in France wears the latest modes, but they look mean anyway.”

See what you can do, and post your sentences here. Happy mathing!

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