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Q: Is the 50th percentile of a distribution the same as the distribution mean?

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The Median is the same as the 50th percentile of a distribution.

Only if the dataset (distribution) you are dealing with in symmetric.

No, it is not.

Answer: 0 The z score is the value of the random variable associated with the standardized normal distribution (mean = 0, standard deviation =1). Now, the median and the mean of a normal distribution are the same. The 50 percentile z score = the median = mean = 0.

The normal distribution.

No they are not the same in a unimodal symmetrical distribution and they will never be

Yes, they can.Yes, they can. In a symmetric distribution they will be the same.

No. The mean and median are not necessarily the same. They will be the same if the distribution is symmetric but the converse is not necessarily true. That is to say, a distribution does not have to be symmetric for the mean and median to be the same. For example, the mean and median of {1, 1, 5, 6, 12} are both 5 but the distribution is NOT symmetric.

If it is a symmetric distribution, the median must be 130.

i agree

That would provide some evidence that the distribution is symmetric about the mean (or median).

That would provide some evidence that the distribution is symmetric about the mean (or median).

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