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Q: Is the uniform probability distribution is symmetric about the mean and median?
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If the mean of a symmetric distribution is 130 which of these values could be the median of the distribution?

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


How to find Median of probability distribution?

how do i find the median of a continuous probability distribution


When you calculate mean is the answer same when the same data is calculated by median?

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.


Can mean and median have same values?

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


Normal distribution is symmetric about mean or median or mode?

Mean


What is the shape of a distribution when the mean and the median are about the same value?

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


What is the shape of a distribution when the mean and the median are the same value?

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


What are some examples where the mean the median and the mode might be the same?

(10, 15, 15, 15, 20) The answer above displays a sample in which the sample mean, sample median and sample mode assume the same value. If you were asking about populations, then the population mean, population median and population mode are the same whenever the probability density function for the population is symmetric. For example, the normal probability density function is symmetric, the t and uniform density functions are symmetric. Many are.


For a symmetric distribution of data the mean is equal to which other quantity?

Median.


Can mean and median have one value?

Yes. And in any symmetric distribution, they will.


What is the relationship among the mean median and the mode in a symmetric distribution?

All equal.


How come the mean is less than the median?

If the distribution is not symmetric, the mean will be different from the median. A negatively skewed distribution will have a mean hat is smaller than the median, provided it is unimodal.