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Yes, the mean (and median and mode) is the 50th percentile of any normal distribution.
Yes, they are. A uniform distribution is one in which the probability of each outcome is the same and, as a result, the mean and median are the same. A uniform distribution should not be confused with a set of random variables, all with the same distributions - much less the same values!For example, the median of a Poisson distribution is not the same as its mean. So if you have a number of random variables (RVs), each with the same Poisson distribution, their mean and median will be different. This is true of any set of RVs whose distributions are asymmetric.And it is very easy to see that the mode need not be the same. The outcome of a single roll of a regular die is the uniform distribution over the numbers {1, 2, 3, 4, 5, 6}. The mean and median are 3.5 but the mode cannot be 3.5 since that is not a value that can ever be observed.
The median is the middle number of any given set when they are in order, least to greatest. If there is an even number of values, the median is the average of the middle two. Ex. (10, 17, 20, 45, 68) The median is 20.
The mean is 0 and the variance is 1. This need not be the case in any other Normal (Gaussian) distribution.
The total area of any probability distribution is 1
If there is any skewness in the distribution.
Yes. And in any symmetric distribution, they will.
Yes, the mean (and median and mode) is the 50th percentile of any normal distribution.
Yes, they are. A uniform distribution is one in which the probability of each outcome is the same and, as a result, the mean and median are the same. A uniform distribution should not be confused with a set of random variables, all with the same distributions - much less the same values!For example, the median of a Poisson distribution is not the same as its mean. So if you have a number of random variables (RVs), each with the same Poisson distribution, their mean and median will be different. This is true of any set of RVs whose distributions are asymmetric.And it is very easy to see that the mode need not be the same. The outcome of a single roll of a regular die is the uniform distribution over the numbers {1, 2, 3, 4, 5, 6}. The mean and median are 3.5 but the mode cannot be 3.5 since that is not a value that can ever be observed.
Together they tell you more about a series of numbers that any one of them. mean - average median - middle number if the numbers are listed from smallest to largest mode - most common number If your mean and median are close to one another, the statistical distribution is usually fairly good. Likewise, if the mode is close to the mean and median, it gives more verification that the distribution is a nice bell curve. The mode is probably the least useful of the three, as it assumes that there are many repeating numbers. In many actual situations, there aren't enough repeating numbers to make the mode of any value.
The median of any single number, such as 616773768287, is itself.
Any number can be a median, so for the correct set of values, 40 could be a median.
12131415161718192021. The median of any single number is just that number.
The median of any set of numbers is its middle value in ascending order
A median divides any triangle in half.
No, it is the name given to the Gaussian distribution.
The median of the factors of any square number is its square root, in this case, 4.