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Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
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Can mean and median have one value?
Yes. And in any symmetric distribution, they will.
Is median used for when there is a wide range of numbers?
If the wide range is evenly spread between the very small and the very large (the distribution is symmetric) then there is not much to choose between the median and the mean. If not, the median will have some advantages as a measure of central tendency.
How to find Median of probability distribution?
how do i find the median of a continuous probability distribution
Why it is important to determine the shape of data distribution before computing descriptive statistics?
You may be most familiar with the normal distribution (the Bell-shaped curve). The mean, mode and median of this distribution are all the same because it is symmetric. If, however, you take a sample from a distribution that is asymmetric in some way then the mean, mode and median will differ. You would need to decide which of these more effectively characterises the population. Then you would compute that descriptive statistic.
Does mode equal median in a normal distribution?
Yes, mode equals median in a normal distribution.
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.
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.
Is the uniform probability distribution is symmetric about the mean and median?
yes
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).
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.
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.
What is the relationship among the mean median and the mode in a symmetric distribution?
All equal.
What is the relation between mean median and mode?
In a symmetric distribution, the mean and the median are the same. Otherwise there is no relation. In symmetric distributions with only one mode, the mode will coincide with the mean and median, but otherwise there is no relation.
