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Classic Median Problem

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Classic Median Problem

by Kumar007 » Wed Apr 01, 2009 10:42 am
Amount Earned Per Day(USD) 96 84 80 70 48
Number Of Days 4 7 4 3 2

A student worked for 20 days . For each of the amounts shown in the first row of the table , the second row give the number of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

A) $96
B) $84
C) $80
D) $70
E) $48

The answer is B . Can someone explain me the answer because i selected C as my choice.
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Re: Classic Median Problem

by skang357 » Wed Apr 01, 2009 10:58 am
Kumar007 wrote:Amount Earned Per Day(USD) 96 84 80 70 48
Number Of Days 4 7 4 3 2

A student worked for 20 days . For each of the amounts shown in the first row of the table , the second row give the number of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

A) $96
B) $84
C) $80
D) $70
E) $48

The answer is B . Can someone explain me the answer because i selected C as my choice.
Dude this is a easy question.

Questions like this the GMAT CAT starts asking you if you get the questions before it wrong.

But even with that said, I doubt the GMAT will ask you a question like this because the actual questions are much harder.

You know that the median value of 20 is going to be the average of the 10th and 11the values after they are lined up in increasing order.

You look at the two rows from right to left as you can see they increase from right to left (at least for the dollars earned).

So you figure out what the 10th and 11th values are going to be.

Looking at the row of the number of days worked for each dollar amount, you can figure out that the 10th and 11th values are going to fall in the 7 days where the guy worked to make 84 dollars per day.

The average of 84 and 84 is 84, answer B.

By the way, know what a mode is. I took real thing yesterday and one question asked me something where I had to know what mode is.

I remember it being the most frequent value in a series of numbers and answered it that way, but I could be wrong.
Impossible is nothing
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by Kumar007 » Wed Apr 01, 2009 1:11 pm
Thanks for wonderful explanation.
Mode is the item which is most often found in given set of observation.
For ex for the observation 1,2,1,2,3,2,3,4,5,2,3,4
Mode = 2

There is a formula for Mode .
Mode = 3*Median - 2*Mean(This formula is valid for the distribution which are moderately symmetric)
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