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PS - Looking for easy calculation trick

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PS - Looking for easy calculation trick [#permalink]

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New post 16 Feb 2009, 21:14
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4 students - 96
7 students - 84
4 S - 80
3 S - 70
2 S - 48

Whats median of 20S(students)?

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 16 Feb 2009, 21:22
84

try to arrange them in ascending order, we are intersted in 10th and 11th items, first 9: 4 S - 80 ,3 S - 70 , 2 S - 48, so 10th and 11th are from group of 84

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 20 Feb 2009, 18:10
I did not understand the Q. Can you please explain better?

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New post 20 Feb 2009, 18:14
I mistook median and mean... If it was mean...I was looking for an easy way to calculate it.

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 21 Feb 2009, 02:17
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There is a trick to calculate mean..it may or may not be the fastest based on the problem but its good to know. Using your example

4 x 96
7 x 84
4 x 80
3 x 70
2 x 48

Guesstimate the mean by looking at the numbers...in this case lets guess that the mean is 80.
Now subtract 80 from each number

4 x (96-80) = 4 x 16 = 64
7 x (84-80) = 7 x 4 = 28
4 x (80-80) = 4 x 0 = 0 0
3 x (70-80) = 3 x -10 = -30
2 x (48-80) = 2 x -32 = -64

Adding them (64-64+0+28-30) = -2
Divide this by 20 =-2/20 = -0.1

Now go back to the guesstimate and add this number to it = 80+(-0.1) = 80 - 0.01 = 79.9

I have gone here in much detail to explain how it works but a lot of this can be done in your mind and find a mean much faster. Hope this helps.

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 21 Feb 2009, 02:37
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Good point, nookway
+1

There is another trick that could help you to deal with mean:

Let's say we have 3 pencils at $12.35 per pencil and 7 pencils at $12.55 per pencil. What is the mean price?

delta = 12.55 - 12.35 = 0.20

mean = 12.35+7/(3+7)*0.20=12.35+0.14=12.49
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New post 21 Feb 2009, 06:28
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Awesome ones, nookway and walker! +1 each. :-D
Walker, I believe your method is good for mixture problems as well? :idea:

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 21 Feb 2009, 07:09
Hm... You are right!
+1

Let's say we have 3 liters of 27.5% solution and 5 liters of 43.5% solutions. What is concentration of the mixture?

delta = 43.5-27.5 = 16.0

result = 27.5 + 5/(3+5)*16.0=37.5%
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New post 21 Feb 2009, 09:18
walker wrote:
Hm... You are right!
+1

Let's say we have 3 liters of 27.5% solution and 5 liters of 43.5% solutions. What is concentration of the mixture?

delta = 43.5-27.5 = 16.0

result = 27.5 + 5/(3+5)*16.0=37.5%



This can be very useful. I have always hated the mixture problems.

Can you please explain how you are doing this and why you are calculating the delta?

How does this work, if there are three different solutions A,B,C?

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Re: PS - Looking for easy calculation trick [#permalink]

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New post 22 Feb 2009, 14:29
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Mixture 1:
x - amount
a - concentration

Mixture 2:
y - amount
b - concentration

Mixture 1+2:
z - amount
c - concentration

z= x+y
c = (a*x+b*y)/(x+y) = (a*x+a*y-a*y+b*y)/(x+y) = a + y/(x+y) * (b-a)

For A,B,C we can apply this method for any two, let's say A and B, and then we can apply the method for new mixture and C.
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Re: PS - Looking for easy calculation trick [#permalink]

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New post 23 Feb 2009, 18:41
walker wrote:
Good point, nookway
+1

There is another trick that could help you to deal with mean:

Let's say we have 3 pencils at $12.35 per pencil and 7 pencils at $12.55 per pencil. What is the mean price?

delta = 12.55 - 12.35 = 0.20

mean = 12.35+7/(3+7)*0.20=12.35+0.14=12.49


That's a good one. Need to save it for future reference.

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Re: PS - Looking for easy calculation trick   [#permalink] 23 Feb 2009, 18:41
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