Indiana Mathematics Initiative

[Estelle Griggs]

My children enjoy Everyday Math so much and are doing great things with it. I like to point out uses in every day life for the concepts we are presenting and cannot for the life of me think of a time that I ever used the median. Do any of you have a real life experience where you used the median? An average, yes, but the median? Please respond if you have an answer. Thanks.
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Estelle Griggs
Grade 2

[John LaMaster]

The mean and median can both be useful measures of the "typical" value of a data set, and often they are close to the same number. However, the median may be a better measure when there is an outlier, or a value which is much larger or smaller than the others. Here’s an example to illustrate.

A teacher pays five groups of students, A, B, C, D, and E for doing roughly the same amount of work at a school event. Each student in groups B, C, D, and E is compensated $10. However, one student in Group A (the teacher's pet?) was paid $46 while the others in Group A were paid $1. See the picture below.



Students in Group A cry foul.
In reply, the teacher asks each group to use the arithmetic mean to describe how much their group was paid on the average. All groups report the same amount of $10 – even Group A, since (46 + 1 + 1 + 1 + 1)/5 = 10.

If Group A finds their median value, it’s only $1. Notice that the median and mean are the same ($10) for Groups B, C, D, and E.

For Group A, the median ($1) more accurately describes the typical value that was paid than the arithmetic mean ($10).

When students have been taught how to find both the median and the mean, this example could be simulated by giving each group of students an envelope containing slips of paper with the above amounts, or, if you want more variability, use the following amounts. Again the mean of each set is the same ($10), but the medians are $1, $10, $10, $10, and $10, respectively.



Another option is that these numbers could represent allowances over the same period of time. In Everyday Mathematics Grade 2, this comparison of mean vs. median will have to wait. The median is introduced as a "typical" measure instead of the mean since the median is usually easier to obtain. For more, check out the book What Do You Mean by Average? Means, Medians, & Modes by Elizabeth James (Lothrop, Lee & Shepard Books, 1978), which is also on the EM literature list for Grades 4-6.

I hope this helps!
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John LaMaster
IMI Web Technology Coordinator

[Paulette Tapper]

I am currently a grade three teacher, but dealt with median a great deal in previously in grade 5....the only real world explanation I could ever come up with was that traditional sizes of clothes...small, medium, large...median is the middle....it also helped them remember the term...other than that, I would start creating some examples of it in class occasionally. Children are sometimes frustrated by mean or average because that number can skew data, and not give anyone's actual answer...if it is the median...someone's real piece of data was often chosen...maybe line them up by tool kit numbers, let your median be line leader for the day...or with two lines, odd and even, find median of each line
As an educator, I just went through a frustrating experience in which IQ testing for Spec Ed indicated that a child did not qualify...do to the mean of his IQ....if we had taken the tests and lined them up with a median...he might have made it...as his reading/language/spelling are low, math is high and skewd his composite score After much wrangling, it was agreed he would retest.

[Mary Lawrence]

I begin teaching median by drawing to four lane highway on the board. Since we are close to an interstate, the children can relate. Well, sort of! My drawings are not always the best! We talk about what the grassy area is in the middle of these lanes of traffic, and we just go from there. It really helps them remember that median means middle!

[Barbara May]

I teach second grade and we begin work on median here. The children love posting their data on sticky notes, lining up in order, and finally sitting down to find the median. As we first line up in order, I emphasize the range since I am aware they will need to know what this is in future years. Concequently, we do this every time we collect data whether it is in math, science, etc. The physical activity of this makes it stick in the children's brain. When they do it in math boxes, they remember it.

[Dianna Lammey]

Paulette,
I like your idea of using actual classroom data for finding the median. Lining students up by tool kit numbers is a great way for them to understand and see how to find it. I have already taught median at this point in the school year, but I will do this as an additional activity throughout upcoming weeks.
Dianna Lammey
Dixie Bee Elementary
Grade 3

[Mandee May]

I just had my credit checked with the 3 major credit companies because I'm buying my first home (YEA!!). When the mortgage broker pulled the three scores, she used the median score as the one for the interest rate. That's a real life example of using a median. You'd have to make it persoanal to the kids somehow, but it was a "aha" moment for me as an adult! I'd always used the middle of the road as the median analogy!!