50 students of a certain class took a test. How many of them got a sco

Question

50 students of a certain class took a test. How many of them got a score less than 82?

(1) The average score is 82.

(2) The median score is 82.

Showmeyaa · Answer

1) Average score of 50 students = 82
Total score of 50 students = 410
Doesn't help - Insufficient!

2)Median = 82
Which means  \frac{25th student's score + 26th student's score}{2} = 82 
25th student's score + 26th student's score= 164
 Case1: 
25th student's score = 26th student's score = 82. In this case, number of students who got a score of less than 82 = 24
 Case2: 
25th student's score = 81, 26th's score = 83. In this case, number of students who got a score of less than 82 = 25
Insufficient!
Even after combining, it is insufficient. Hence, (E)

RiyaJain69 · Answer

Why isn't this one's answer C? When we combine both the statements, we learn that mean = median. And we know that mean and median are equal only when all the values in the set are equal. So if we combine statements 1 and 2, we get our answer, that nobody scored less than 82 since all of them scored exactly 82. So answer should be C.
Am I wrong somewhere?  Bunuel , would greatly appreciate your insights. Thanks in advance!

Showmeyaa · Answer

Hi  RiyaJain69 , though the question is not directed at me. Let me still try to answer this.

If mean = median, it means that the distribution is symmetric. The set could have:
1)Consecutive numbers
2)Same numbers
Hence, the answer is (E)!

IanStewart · Answer

That's actually not quite right. It's true (and useful to know) that if a distribution is symmetric, then the mean and median are always equal. So for example, in any equally spaced set (1, 3, 5, 7, 9, say) the mean and median are equal, and in any other symmetric list (1, 1, 2, 8, 9, 9, say, or when every element is the same) the mean and median will also be equal. But the mean and median can be equal in all kinds of other situations as well. So in this set, which is not symmetric:

0, 2, 10, 11, 27

the mean and median are both 10.

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50 students of a certain class took a test. How many of them got a sco

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50 students of a certain class took a test. How many of them got a sco

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