SOLUTION: What is the median of 80,80,80,80,80,85,85,85,85,85,90,90,90,90,90

Question 1205795: What is the median of 80,80,80,80,80,85,85,85,85,85,90,90,90,90,90

Found 3 solutions by MathLover1, math_tutor2020, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

80,80,80,80,80,85,85,||,85,85,90,90,90,90,90
the median is
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answer: 85

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Explanation

Method 1

The first task is to sort the values. Thankfully that has already been done for us.
Always 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,
85,85,85,85,85,
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
80,80,80,80,80,85,85,85,85,85,90,90,90,90,90
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 85 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
~~80,80,80~~,80,80,85,85,85,85,85,90,90,~~90,90,90~~
80,80,85,85,85,85,85,90,90
~~80,80,85~~,85,85,85,~~85,90,90~~
85,85,85

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.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

You don't need to go into much detail to answer the question if you know what "median" means.

The set of data consists of 5 each of 3 distinct values, so there are equal numbers of values above and below the middle value. That means the median is the middle value.

ANSWER: 85

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