Table with scores and frequency is given. How to find the median that exceeds the mean of the marks.

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[My approach to this question is:

I have taken out mean which is 69.3 (Please verify) and then I took out median (68.178) and then I took difference but the answer is not falling in given options. I am having doubt whether I have done it in right way or not?

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Assuming you are supposed to calculate the mean multiplying the frequency by the middle of the interval i.e. if $ mean = \frac{(45*12) + (55*21) + (65*32) + (75*29) + (85*25) + (95*9)}{128} $

Then you get an average of $ 69.765625 $

And assuming the 64th and 65th element are both 69, the median would be 69.

From the information given, the choice I would personally choose would be D) none of the above since the median is below the average

But really, the information is inconclusive with the maximum difference occurring when the median is 69 and mean is 64.90625 and the minimum difference occurring when the median is 60 and the mean is 71.5859375