Q&A #19095

Mean, median, mode in grade 3

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From: Ralph (for Teacher2Teacher Service)
Date: Nov 23, 2007 at 21:42:41
Subject: Re: Mean, median, mode in grade 3

Dear Jennifer,

Thank you for writing to T2T.  I'm kind of surprised that a Grade 3
curriculum would have students dealing with all 3 measures of central
tendency (mean, median, and mode), but let's go through some examples to
hopefully help you make sense of when different measures might be used.  In
the example you gave, there are so few data points that I'm not sure ANY
measure of "average" is needed, but let's go through it, anyway.

The actual NUMBERS you're dealing with are the number of children in each
case, so you have 2, 4, 4, and 5  (regardless of what "food" they're attached
to), so:  The MODE would be 4, the NUMBER that occurs most frequently in the
data set.  The MEDIAN would also be 4, since the two middle numbers are both
4.  The MEAN would be the sum of all the numbers, divided by how many numbers
there are,  so (2 + 4 + 4 + 5) divided by 4, or 15/4, or 3 3/4.

You asked what the purpose of the median is, and I'll admit that it's hard
to make sense of it at a "Grade 3 level" (which is why it usually isn't
taught until later). It can be useful if you have a set of data where there
is an EXTREME number or two that could "throw off" the Mean. For example,
let's say the numbers in the set were  2,4,4,5,6,7 and 1000.  The mode would
be 4 (there are two of them, and only 1 of all the other numbers), the median
would be 5, it's the middle number, and both of those are "reasonable
representations" of the "center" or "average" of the set, but if you were
to find the mean, it would be (2 + 4 + 4 + 5 + 6 + 7 + 1000)/7.
1028/7 or about 147, which is NOT a really good indication of the "center"
or "average" number in the set.  In this case, the median is a much better
indicator of the "average" number in the set.

Hope this helps,

 -Ralph, for the T2T service

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