A certain school has 250 students. All these students took a psychomet

Question

A certain school has 250 students. All these students took a psychometric test that scored them on a scale 1 to 10. Is the average score of these students greater than the median score?

(1) At least 140 students scored less than average
(2) Sum of all the scores is 360 times Median score

IanStewart · Accepted Answer

If you list the scores in increasing order, the median here will be the average of the 125th and 126th highest scores. If we know 140 scores were below the average, the 125th and 126th highest both must be, so the median must be, and Statement 1 is sufficient.

If S is the sum of the scores, S/250 is the average score. If M is the median, Statement 2 tells us S = 360M, so M = S/360. S/250, the average, is definitely larger than S/360, the median, since it has a smaller denominator (and since S is positive). So Statement 2 is also sufficient.

The answer is D.

Anulitha · Answer

I get how 2 answers the problem (average is greater than median) but how does 1 explain it?

Posted from my mobile device

ConfusedSEA · Answer

Important theory: The mean = median if in any arithmetic progression.

(1) At least 140 students scored less than average
Median is the 126th term. Since at least the 140th term is less than average,  Median < Average .

(2) Sum of all the scores is 360 times Median score
Median < Average

pierjoejoe · Answer

the median is the 125th term + 126th term divided by 2
the average is the sum of all terms divided by 250

(1) more than 140 students have scored less than average. this means that less than 110 students scored more than average.
the distribution will look something like this:
less than average | more than average
at least 140 | less than 110 students

less than average  
 more than or equal to average  
 
  frequency  
 more than 140 
 less than 110

minimum --------> average --------> maximum
from minimum to average there are more than 140 people
from average to maximum there are less than 110 people 
Given that the 125th and 126th terms MUST be both in the range from "0" to AVERAGE (because there are AT LEAST 140 people below average)
than we can conclude that the median MUST be less than average
(SUFFICIENT) 
(2) this is telling us the relationship between median and average (SUFFICIENT)

vektr · Answer

So, we are given 140 students are below the average score.

The median is supposedly middle value when arranging all the numbers in ascending/descending order.
And we know there are total 250 people.

=> If we align them on ascending/descending order, median would be mean of 125th & 126th students.

Therefore, 125th & 126th students have to have score below mean (infact till 140th student everyone will have score below average score).

So we know Mean > Median

A certain school has 250 students. All these students took a psychomet

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	less than average	more than or equal to average
frequency	more than 140	less than 110

GMAT Data Sufficiency (DS) Questions

A certain school has 250 students. All these students took a psychomet

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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