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The median is the value that separates a data set into two parts. Half of the values in the data set will be less than the median and the other half
will be greater than the median. In order to calculate it, you first start with your dataset and arrange the
values in order from the smallest to largest values. So in this dataset, we have a 2, 7, 4, 3, and 5. And if we
arrange them from low to high, we'll then have 2, 3, 4, 5 and 7. And you'll notice that if we just walk our way in from the outer edges to the middle of the
set, there's a data value that occupies the middle position. And, in this case,
that is the number 4. If you'll notice, there are two values in the set that are smaller than the 4 and two values
that are higher, or larger, than the 4. Now, we happened just to have had an odd number of data values in this set.
And so, things get a little trickier when I have an even number of data values there. So, in that case, I have to do a little more work.
Here's a data set that has six values in it: 4, 6, 3, 10, 12 and 15. I start the same way, by putting the data in order from low to high. If
I do that, I'll have 3, 4, 6, 10, 12, and 15. And if I use the same
technique of walking from the outer edges of the data to the middle, I no longer have a single value that sits in the middle, I have two. And so, what I'll
do it take those two center values and calculate their mean. In this case, that's the 6 and the 10. Well, how would I calculate the mean of those two
values? I would add them together, then divide by 2. So 6 plus 10 is 16, divided by 2 is 8. You might notice
that 8 sits halfway between the 6 and the 10. And thus, three values are smaller than the 8 and three values would be larger than the 8. So, the 8 is the
median and splits the data set into two parts. So the median for this set is the 8.