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# Lena’s first test score was at the 80th percentile in a

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Lena’s first test score was at the 80th percentile in a [#permalink]  01 May 2012, 09:14
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Is there any formula about Percentile and percentile ranks

Lena’s first test score was at the 80th percentile in a class of 120 students. On another test, 24 out of 200 students scored better than Lena. If nobody had Lena’s score, what is Lena’s percentile after the two tests?

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0A is 85TH
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Re: percentile [#permalink]  01 May 2012, 12:28
(120*80%+200-24)/(120+200)=85
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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  01 May 2012, 14:08
keiraria wrote:
Is there any formula about Percentile and percentile ranks

Lena’s first test score was at the 80th percentile in a class of 120 students. On another test, 24 out of 200 students scored better than Lena. If nobody had Lena’s score, what is Lena’s percentile after the two tests?

best regards

0A is 85TH

ORIGINAL QUESTION IS:

Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

If someone's grade is in x_{th} percentile of the n grades, this means that x% of people out of n has the grades less than this person.

So, being in 80th percentile out of 120 grades means Lena outscored 120*0.8=96 classmates.

In another class she would outscored 200-24=176 students.

So, in combined classes she outscored 96+176=272. As there are total of 120+200=320 students, so Lena is in \frac{272}{320}=0.85=85%, or in 85th percentile.

The concept is explained here: math-number-theory-percents-91708.html

Hope it helps.
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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  08 Oct 2012, 13:14
Nitpicking, but if 24 students scored better then Lena, then wouldnt she have scored better than 200 - 25 = 175 students?

We should count her score as well?

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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  08 Oct 2012, 15:03
manwiththeharmonica wrote:
Nitpicking, but if 24 students scored better then Lena, then wouldnt she have scored better than 200 - 25 = 175 students?

We should count her score as well?

Posted from my mobile device

There are two categories: one, the students who scored better than Lena, so their scores are definitely greater than her scores; two, those who didn't score better then Lena, so their scores are less than or equal to Lena's scores. Lena, herself is in the second category. The information that nobody has Lena's score is not relevant. What is important is how many outscored her:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.
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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  08 Oct 2012, 22:08
EvaJager wrote:
manwiththeharmonica wrote:
Nitpicking, but if 24 students scored better then Lena, then wouldnt she have scored better than 200 - 25 = 175 students?

We should count her score as well?

Posted from my mobile device

There are two categories: one, the students who scored better than Lena, so their scores are definitely greater than her scores; two, those who didn't score better then Lena, so their scores are less than or equal to Lena's scores. Lena, herself is in the second category. The information that nobody has Lena's score is not relevant. What is important is how many outscored her:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.

Hi Eva,

I am still not convinced with the above explanaton. Can you please explain again?
Its clearly written in the question that 24 students out of 200 scored better than Lena means she scored better than 175 students !! (Please correct me)

Thanks
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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  08 Oct 2012, 23:01
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154238 wrote:
EvaJager wrote:
manwiththeharmonica wrote:
Nitpicking, but if 24 students scored better then Lena, then wouldnt she have scored better than 200 - 25 = 175 students?

We should count her score as well?

Posted from my mobile device

There are two categories: one, the students who scored better than Lena, so their scores are definitely greater than her scores; two, those who didn't score better then Lena, so their scores are less than or equal to Lena's scores. Lena, herself is in the second category. The information that nobody has Lena's score is not relevant. What is important is how many outscored her:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.

Hi Eva,

I am still not convinced with the above explanaton. Can you please explain again?
Its clearly written in the question that 24 students out of 200 scored better than Lena means she scored better than 175 students !! (Please correct me)

Thanks

There were two tests. What is important is how many outscored her on both tests:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and they represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.
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Re: Lena’s first test score was at the 80th percentile in a [#permalink]  09 Oct 2012, 01:03
Got it thanks !!
Kudos for you !!
Re: Lena’s first test score was at the 80th percentile in a   [#permalink] 09 Oct 2012, 01:03
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