If the median of first 40 students score is 74 and last 65

Question

If the median of first 40 students score is 74 and last 65 students score is 78, then what is the median of all 115 scores?

OA is 78

Capricorn369 · Answer

What is the source of this question becasue one critical point is missing in this question.
The question must say that all the 115 scores are in ascending order otherwise the question is not solvable.

Now, considering 115 scores are in ascending order the median will be 58th score. Accoring to question the last 65 students score is 78.
Because 58th score falls under these 65 students's score. Answer is 78.

Cheers!

g3kr · Answer

I do not know the source. It was in a material i have. I think it means the median of the last 65 scores is 78. then what is the median of all 115 scores?

KarishmaB · Answer

No, it doesn't mean that the median of last 65 scores is 78. It means that the last 65 scores are 78 each.

The median of the first 40 scores is 74 so 74 is the avg of the 20th and the 21st score (assuming the scores are in ascending order).
We have no information on the 10 scores from 41st score to the 50th score.
The last 65 scores (from 51st score to the 115th score)

So the scores probably look something like this:
72, 72, 72, 73, 73, .........74, 74, 74, 74, .....75, *, *, *, *, *, *, *, *, *, *, 78, 78, 78, 78, 78 , 78, 78.....

The median of 115 scores will be given by the 58th score when all the scores are in ascending/descending order. 
The 58th score will be 78 so median must be 78.

If instead, the median of last 65 scores were 78, we wouldn't know the 58th score and we wouldn't have been able to find the median.

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If the median of first 40 students score is 74 and last 65

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If the median of first 40 students score is 74 and last 65

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