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# Lena’s grade was in the 80th percentile out of 120 grades in

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01 May 2012, 09:14
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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?
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01 May 2012, 12:28
(120*80%+200-24)/(120+200)=85
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01 May 2012, 14:08
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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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08 Oct 2012, 13:14
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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
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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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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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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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09 Oct 2012, 01:03
Got it thanks !!
Kudos for you !!
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17 Nov 2013, 08:25
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19 Nov 2014, 01:45
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11 Jan 2015, 05:34
Hi,

Great, but did the problem also give answer options? It is quite good to see what the offered answers are in order to get an idea of how test makers would trick you into giving the wrong answer!
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13 Sep 2015, 04:43
Sorry, but there still seems to be some discrepancy. If xth percentile means that x%people score BELOW you then with that explanation, EITHER (1) should be - 96 scored below so Leena was 97th and thus 23 people outscored her.
OR that Leena was 175th and she outscored 174, so overall percentile will be (174+96)/320.

Bunuel or EvaJager, can you help me understand this/confirm if my reasoning is right?
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08 Nov 2016, 17:26
Bunuel wrote:
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.

Hi Bunuel,

In reference to number of students she outscored in second class (highlighted in red), shouldn't that number be 175 instead? (because 24 students scored more than her, she herself is 25th highest scorer and the remaining class of 175 student are the ones who scored less then her).

Although, working with 176 makes calculation easier by quickly reducing the fraction to 17/20 which is clearly .85

I am just trying to understand the correct logic for working with percentile. Will really appreciate your help.

Thanks!
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14 Dec 2016, 15:41
Students with score greater than Lena in class A=> 20/100 *120 => 24

Students with score greater than Lena in class B => 24

Combined class strength = 120+200 = 320

Students with score greater than Lena in class A=> 20/100 *120 => 24

Students with score greater than Lena => 24+24 = 48

48 is 15 percent of 320
Hence Lena's percentile rank => 85

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15 Feb 2017, 21:42
keiraria wrote:
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 Lena's score is 80%, then she has outscored : (80*120)/100 people, i.e., 96 people.
Thus, 24 people have a score greater than her in her own class.

Also, in the other class there are another 24 people who would outscore her, making it a total of 48 people to outscore her.

(48*100)/320 = 15 % people to outscore her.

Thus, Lena's score would be 85% overall.

B.
Re: Lena’s grade was in the 80th percentile out of 120 grades in   [#permalink] 15 Feb 2017, 21:42
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