Means, Ranges, and Medians, and Mode

    Visual learners need "silly" things to help them learn.  I was subbing in a third grade GT class, when this math subject came up.  Even some of those kids were looking lost.  I gave them a silly story to help them remember each term.  Let's start with RANGE.  The first thing,  I told them, was to think of a song with the word RANGE in it.  Of course, they answered, "Home, Home On The Range." 
    "What is an animal you'd most likely see on a range?" I asked.
    " A cow," they all replied.
    So, think of the numbers you have to find the RANGE for as cows.  Line up all the cows to come in for milking time.  Put the smallest ones first, as they are the hungriest.  Put the largest ones last.  If given the numbers 2, 18, 4, 9, 1  then the new order for these would be: 1,2,4,9,18.  (Putting them in order is the most important concept).  Then just subtract the smallest cow (number) from the largest cow (number).  In this example it is 18-1.  The RANGE is 17.  

   The second concept is MEAN.  I suppose it's not nice to call a teacher "mean," but we've all done it when he/she pops a test on us.  So, I use this as a way to teach the concept.  I tell the kids that the MEAN teacher is giving us a test.  I want to figure out what I need to get on this test to keep my grades up, or just to find out what grade I already have.
My past tests scores were:  84 + 60 + 74 + 90 .  They total 308.  I divide by the number of tests. 308 divided by 4  equals a 77 (because I had scores from 4 tests).  I need to study a little harder. 
   In the top (cow) example, the mean is 1+2+4+9+18=34.  Divide this by 5 tests to get: 6.8


                                      

  The above photo is of a  highway MEDIAN.  The kids have all seen these.  Show them the picture.  Remind them that it goes right down the middle of the road.  Just like this highway median, a math median goes right down the middle of the numbers. Using the cow numbers because you must also put them in order to find the median, you have
                               1,2,4,9,18   the median is 4 which is the number in the middle.

  If the numbers, for example were 13, 18, 13, 14, 13, 16, 14, 21, 13 ,  you would put them in order as 13, 13, 13, 13, 14, 14, 16, 18, 21.  Counting in from both sides to the middle (or median in the road) the answer is 14.

 Finally, the mode.  I tell the kids that MODE means the most.  In punk rock terms, this guitarist might say "MO."  As in "I want some mo of that."  I don't know why this sticks, but it is just silly enough for them to remember.    In the numbers 1,2,4,9,18 this is no mode because none of the numbers are repeated.  In the numbers 13,13,13,13,14,14,16,18,21 The number 13 shows up "mo" than the others, so it is the mode.