A certain list consists of 400 different numbers. Is the average......

Question

A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?

(1) Of the numbers in the list, 280 are less than the average.
(2) Of the numbers in the list, 30 percent are greater than or equal to the average.

chetan2u · Accepted Answer

400 different numbers... Median = average of 200th and 201st....

(1) Of the numbers in the list, 280 are less than the average. 
here 280 are less, so ofcourse 200th and 201st will also be less than average...
ans YES
Suff

(2) Of the numbers in the list, 30 percent are greater than or equal to the average 
30% of 400 = 120 so ONLY 120 are greater than average, same as above 
Suff

D

ScottTargetTestPrep · Answer

We need to determine whether the average (A) of the 400 numbers in the list is greater than the median (M). Note that since there are 400 numbers in the list, the median is the average of the numbers in the 200th and 201st spots when the numbers are listed in increasing order.

Statement One Alone:

Of the numbers in the list, 280 are less than the average.

Since 280 of the 400 numbers are less than the average, the numbers in the 200th and 201st spots are both less than A. Therefore, the median M is less than the average A. Statement one alone is sufficient to answer the question.

Statement Two Alone:

Of the numbers in the list, 30 percent are greater than or equal to the average.

Since there are 400 numbers in the list, this statement is actually saying (0.3)400 = 120 numbers are greater than or equal to the average, which is equivalent to saying 400 - 120 = 280 numbers are less than the average. By our analysis of statement one, we already know that this information is enough to answer the question. Statement two alone is sufficient to answer the question.

Answer: D

MathRevolution · Answer

If the original condition generally includes “rElation” of median, mean, standard deviation, etc, there is high chance that E is the correct answer. 
Using both the condition 1) and the condition 2), we know 1)=2). Hence, the correct answer is D. 
So, there always is a median in 280 numbers, and median<mean. The answer is yes and the condition is sufficient.
Please remember that if 1)=2), then D is the correct answer with 95% of chance.

hannahkagalwala · Answer

Hi, why do we assume that all the numbers are arranged in order even though it is not mentioned?

Sent from my A0001 using  GMAT Club Forum mobile app

chetan2u · Answer

Hi,
We just know that numbers are different..
When we talk of median, we have to arrange these numbers in ascending or descending order..

Here too it may not be given but we have to arrange these in ascending or descending order before moving ahead.

dave13 · Answer

hello chetan2u

nice explanation. i wonder if there is any rule that is relevant to the relation between median and arithmetic mean ? i mean the correlation ... for instance you say only 120 are greater than average ... what if it were 50 / 50 ?

another question 120 numbers could be large numbers for example 280 numbers could be 1, 2, 3 9, 7, etc and 120 number could be starting from number 900 and higher.... thanks and have a great weekend

pushpitkc hi there

any idea on the above solution ?

thanks

pushpitkc · Answer

Hi  dave13

Unfortunately, there is no correlation between median and mean

Consider a set A = {1,1,1,1,1} which has a median and mean of 1
Another set B = {1,2,3,6,8} has median of 3, but mean of 4

So as you see, for different sets, the mean and median may not correlate

Hope this helps you!

BrentGMATPrepNow · Answer

Given : A certain list consists of 400 different numbers.

Important: If we have an EVEN number of values, then the median = the average of the two middle most values (once the numbers are arranged in ascending order)  
So, if we arrange all 400 numbers in  ascending order , the median = (the 200th value + the 201st value)/2

Target question :    Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?

Statement 1 : Of the numbers in the list, 280 are less than the average.  
Let's let A = the average of the 400 numbers
So if we arrange all 400 numbers in ascending order, the first 280 numbers are less than A.
This means the 200th value is less than A, and the 201st value is less than A.
If the 200th value and the 201st value are each less than A, then the average of the 200th value and the 201st value must be less than A
In other words, (200th value + 201st value)/2 < A
The answer to the target question is  YES, the average of the numbers IS greater than the median of the numbers 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : Of the numbers in the list, 30 percent are greater than or equal to the average 
This also tells us that 70% of the numbers are LESS THAN the average. 
70% of 400 = 280
So, statement 2 is indirectly telling us that, among the numbers in the list, 280 are less than the average.
In other words, statement 2 is indirectly telling us the SAME THING statement 1 tells us. 
Since we already concluded that statement 1 is sufficient, we can also conclude that statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
RELATED VIDEO
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

Basshead · Answer

A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?

My approach: 
The two statements say the same thing. Thus if we had to guess, the answer must be D or E.

(1) Of the numbers in the list, 280 are less than the average.

If 280 are less than the average, then the median (the number between the 200th and 201st) MUST be less than the average. SUFFICIENT.

(2) Of the numbers in the list, 30 percent are greater than or equal to the average.

If 280 are less than the average, then the median (the number between the 200th and 201st) MUST be less than the average. SUFFICIENT.

Answer is D.

Hoozan · Answer

Similar question: https://gmatclub.com/forum/in-city-x-la ... 35552.html

adityaganjoo · Answer

Need your help in Statement 2
We know nothing about the rest 70%. What if they are also equal to the average and the 30% mentioned here are also equal to the average (Statement 2 states 30% are greater than or equal to average)
In that case, mean would be equal to the median.
But in many other cases, it won't

Please help!

IanStewart · Answer

If a GMAT sentence says "30% of the animals in the zoo are frogs", that always means "exactly 30% of the animals are frogs", so you can then conclude "70% of the animals are not frogs". So in this question, when Statement 2 says "30% are greater than or equal to the average", that means "70% are less than the average", and Statement 1 and Statement 2 say the same thing.

That's not even to mention that in this question, the values cannot all equal the average, because all 400 values are different. At most one value in the set can be equal to the average.

Posted from my mobile device

bumpbot · Answer

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A certain list consists of 400 different numbers. Is the average......

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