The frequency distribution of student scores on a test is as shown abo

Question

https://gmatclub.com/forum/download/file.php?id=48797 The frequency distribution of student scores on a test is as shown above. How many of the scores are above the class average? A. 9 B. 10 C. 11 D. 12 C. 13 2019-07-08_1351.png

nick1816 · Accepted Answer

IMO we don't even need the class average to solve this question.
Number of students that are above the class average can be 1,3,6, 8,  12 , 16, 17 or 19

IMO D

BrentGMATPrepNow · Answer

Awesome solution nick1816 !!! Your approach so outside the box, I forgot where the box is altogether!!

Kudos for you!!

nick1816 · Answer

Thanks a lot Sir. This kinda comment from you means a lot to me.

Archit3110 · Answer

total avg score of 9 subjects ; 732/ 9 ; 81.3
so students >81.3 score are above avg ; 4+2+3+2+1; 12
IMO D

Archit3110 · Answer

nick1816 
liked your approach but its more of hit and trial ; though in case of two close options this approach would have been difficult

nick1816 · Answer

It's not a hit and trial approach. I always find cumulative frequencies firstly, if the question has similar stem as that of this question. It hardly takes 10-15 secs to calculate them and a lot of times you get the answer right away, as you saw in this question. But if there were 2 cumulative frequencies present in the options, then i would have calculate the average. Always keep it in mind that GMAT aint testing your calculation skills; it's more often gonna test your logical thinking skills.

adkikani · Answer

Hi  nick1816   GMATPrepNow   VeritasKarishma   MentorTutoring

Can you elaborate your approach please? How to find cumulative frequencies and the set of numbers you derived?

nick1816 · Answer

Number of students that score 95 or 95+ = 1

Number of students that score 94 or 94+ = 1+2 =3

Number of students that score 90 or 90+ = 1+2+3=6

Number of students that score 85 or 85+ = 1+2+3+2=8

Number of students that score 83 or 83+ = 1+2+3+2+4=12

Number of students that score 79 or 79+ = 1+2+3+2+4+4=16 (We can stop here, as none of the option is 16+)

Because our average lies between 64-95, our answer must be one of the above.

GMATinsight · Answer

Answer: Option D

Video solution includes two approaches.

https://www.youtube.com/watch?v=kJvACqLZngQ

AndrewN · Answer

Hello,  adkikani , and thank you for tagging me. I worked this one mentally, and I did get the correct answer, even if I should have written down a few numbers to save some time. I took 2:01. Often with  average  questions, I just pick an arbitrary number to be the average and make adjustments as necessary. This process helps me to work with smaller numbers and make fewer errors. Let me explain.

Although I do not know the average, I do not want to figure out a sum and divide by all the students. The numbers are too big. But 80 seems like a reasonable middle value, given the distribution, so for now, I will just keep track of each score relative to my made-up average and tally up that sum instead:

64: -16;  Sum = -16 
70: -10 (*2, since there are two of them) = -20;  Sum = -36 
72: -8;  Sum = -44 
79: -1 (*4) = -4;  Sum = -48 
83: +3 (*4) = +12;  Sum = -36 
85: +5 (*2) = +10;  Sum = -26 
90: +10 (*3) = +30;  Sum = +4 
94: +14 (*2) = +28;  Sum = +32 
95: +15;  Sum = +47

Now I can divide this sum by the total number of students to see how I will need to adjust the average:

\frac{47}{20}

In all honesty, my answer was  a little more than 2 .  That  is just how lazy I can get on PS problems. Anyway, it is clear that the class average needs to be adjusted up, so

80 + a little more than 2

is  82- something  . Good enough. How many students scored an  83 or above ?

4+2+3+2+1=12

Choice (D) it is. I know it might seem like more trouble than it is worth, but trust me, with practice, calculating averages can be a cinch.

- Andrew

BrentGMATPrepNow · Answer

https://i.imgur.com/5Ig05Qo.png

Let's examine a few cases.

If it were the case that the average score is 94.5, then  1  score is greater than the average
If the average score were 93, then  3  scores are greater than the average (1 + 2 =  3 )
If the average score were 89, then  6  scores are greater than the average (1 + 2 + 3 =  6 )
If the average score were 84, then  8  scores are greater than the average (1 + 2 + 3 + 2 =  8 )
If the average score were 80, then  12  scores are greater than the average (1 + 2 + 3 + 2 + 4 =  12 )
If the average score were 78, then  16  scores are greater than the average (1 + 2 + 3 + 2 + 4 + 4 =  16 )
etc..

So, the correct answer could be  1  or  3  or  6  or  8  or  12  or  16  or ...

When we check the answer choices, only one answer choice (answer choice D) is among the possible values.

Answer: D

Cheers,
Brent

KarishmaB · Answer

The numbers given in this question are extremely simple. I thought that the average would be somewhere around 80 but to the right since more people seem to be on the right. Now, the point was only whether 4 people of 83 are more than the average or less. If they are more than average, our answer would be 12, else it would be 8. But 8 is not in the options so

Answer (D)

If the numbers in the question were not so simple, I would have assumed the average to be 81.
79 and 83 have 4 people each so their deviation cancels out. 
72 and 90 are equidistant from 81 so 1 person's deviation is cancelled.
70 is 11 less than 81 so deviation of 2*11 and 64 is 17 less than 81 so deviation of 17 gives a total negative deviation of 39.

Meanwhile, 85 is 4 more than 81 so deviation of 2*4 and 90 is 9 more than 81 so deviation of 2*9 and 94 is 13 more than 81 so deviation of 2*13 and 95 is 14 more than 81 so deviation of 14. Total positive deviation is 8 + 18 + 26 + 14 = 66

So, in all, it is a positive deviation of 66 - 39 = 27 which means the average is actually 81 + 27/20 = 82.35

bumpbot · Answer

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The frequency distribution of student scores on a test is as shown abo

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The frequency distribution of student scores on a test is as shown abo

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