Question 77065: Find the mean and the median.
-2, -7/4, 3/4, 4, 9
These are my choices. I came up with Mean 2, Median 3/4 but I am not positive.
Mean 2, Median 3/4
Mean 10, Median 2
Mean 2, Median 2
Mean 10, Median 3/4
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You should be more confident in your work ... your answers are correct!
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To find the mean (or average) you algebraically add all the numbers together and divide
by the quantity of numbers you have. In this problem you added:
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and got the total of 10. There are 5 numbers so you divide the total 10 by 5 to find
that the mean is:
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The median is just the middle number when the series is arranged in order that the numbers appear
on the number line ... from left to right. The numbers are already in ascending order as
they were given to you ... as you go from left to right each number is greater than the
preceding number. 3/4 is the middle number in the series. It has two numbers that are
less than it and two numbers that are greater than it. So 3/4 is the median. As long
as the total number of terms in the series is an odd number (in this case 5) there will
be a middle term ... a term that has an equal number of terms below it as there are above it.
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Good job. But let me ask you something about the median if the series has an even number
of terms.
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Suppose you are given the following series ... 2, 4, 6, 8, 10, 12 ... and are asked what
the median is. How do you do that? It can't be 6 because there are only 2 numbers
less than 6 while there are three numbers greater than 6. And it can't be 8 because
there are 3 numbers less than 8 but only 2 numbers greater than 8. The answer is that
you find the two numbers in the middle of the series and average those two numbers.
In this series the pair of numbers in the middle are 6 and 8. Add them together to get
14 and divide 14 by 2 to find that their average is + 7. So the median of this series is
+7 ... a number that doesn't even appear in the series.
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Let me give you another series with an even number of terms and see if you can find the
median (just for practice). The series is:
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-5, -1, 7, 14, 17, 21, 24, 200
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What is the median of this series? The answer is 15.5 and how did I get that?
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(Hint: the middle pair is 14 and 17. Average them.)
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Hope this helps ...
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