Question 1205795
<font color=black size=3>
Answer:  <font color=red size=4>85</font>


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Explanation


Method 1


The first task is to sort the values. Thankfully that has already been done for us. 
<u>Always</u> make sure the values are sorted before attempting to find the median.


The original string of values
80,80,80,80,80,85,85,85,85,85,90,90,90,90,90
rewrites to
80,80,80,80,80,
85,85,85,85,85,
90,90,90,90,90
which I think is easier to see how many items there are. This block of values is 3 items tall and 5 items across. There are 3*5 = 15 values total.


n = 15 is the sample size.
n/2 = 15/2 = 7.5 which rounds to 8
The median is in slot 8
7 values are below it, and 7 values are above it
7+1+7 = 15 values total


The value in slot 8 is 85. It's the 3rd copy of "85" in the second row of this block:
80,80,80,80,80,
85,85,<font color=red size=4>85</font>,85,85,
90,90,90,90,90
Or you can return back to the original string of values to count out 8 positions from the left.


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Method 2


Chop off the first and last values of 
80,80,80,80,80,85,85,85,85,85,90,90,90,90,90
to get
<font color=red><s><font color=black>80</font></s></font>,80,80,80,80,85,85,85,85,85,90,90,90,90,<font color=red><s><font color=black>90</font></s></font>
which cleans up to
80,80,80,80,85,85,85,85,85,90,90,90,90


Repeat the process again to go from
80,80,80,80,85,85,85,85,85,90,90,90,90
to
80,80,80,85,85,85,85,85,90,90,90


Keep this process going until either (a) we end up with one value or (b) we end up with 2 values
80,80,80,85,85,85,85,85,90,90,90
80,80,85,85,85,85,85,90,90
80,85,85,85,85,85,90
85,85,85,85,85
85,85,85
85
We see that <font color=red>85</font> is the middle most value.



Or what we can do is cross off say 3 items at a time from each endpoint. 
This is to help speed things up.
80,80,80,80,80,85,85,85,85,85,90,90,90,90,90
<font color=red><s><font color=black>80,80,80</font></s></font>,80,80,85,85,85,85,85,90,90,<font color=red><s><font color=black>90,90,90</font></s></font>
80,80,85,85,85,85,85,90,90
<font color=red><s><font color=black>80,80,85</font></s></font>,85,85,85,<font color=red><s><font color=black>85,90,90</font></s></font>
85,<font color=red>85</font>,85



Note: If you end up with 2 values tied for the middle, then take the midpoint of them. This occurs only when the sample size is an even number. 
The midpoint formula is (p+q)/2 where p and q are the middle most values.



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Method 3


Use software such as a speadsheet or online calculator.
This method doesn't have much to explain about it, other than it's something I only recommend as a way to check your answer. 
It's best to know how to find the median by hand.
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