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Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable.
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The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist.
The distribution cannot, therefore, be symmetric about something that does not exist.
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In a perfectly symmetrical unimodal distribution is the mode and the median the same as the mean?
No, it is in general not true - for example for uniform distribution on [0,1] every number in the interval is a mode, but the mean is 1/2. The correct answer would be that a symmetric unimodal distribution has one mode equal to the mean (but may have modes elsewhere).
Normal distribution is symmetric about mean or median or mode?
Mean
What is the relation between mean mode median in symmetric normal distribution?
They are all the same.
Can the distribution of the mean median and mode be equal if the are positively skewed or negatively skewed or symmetric?
Not necessarily.
In an uniform distribution is the mean and median the same?
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 mode is the largest value in a symmetric distribution?
Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.
In a perfectly symmetrical unimodal distribution is the mode and the median the same as the mean?
No, it is in general not true - for example for uniform distribution on [0,1] every number in the interval is a mode, but the mean is 1/2. The correct answer would be that a symmetric unimodal distribution has one mode equal to the mean (but may have modes elsewhere).
Normal distribution is symmetric about mean or median or mode?
Mean
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.
What is the relationship among the mean median and the mode in a symmetric distribution?
All equal.
How you get the mode by applying probability distribution?
The mode is the most probable value. Often, you determine the mode by plotting the experimental probability distribution, and finding the peak value. The mode is not necessarily the same as the mean nor the median, unless the distribution is symmetrical.
What is the relationship among the mean median and mode in a symmetric distribution?
They are all equal . . . they are the same.(In an asymmetric distribution they are not 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.
What is the relation between mean mode median in symmetric normal distribution?
They are all the same.
Can the distribution of the mean median and mode be equal if the are positively skewed or negatively skewed or symmetric?
Not necessarily.
A distribution with a shape that is symmetrical around the mean with a bell shape is described as?
The distribution described is a normal distribution. It is characterized by a symmetric bell-shaped curve where the mean, median, and mode are all equal and located at the center of the distribution.
In an uniform distribution is the mean and median the same?
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.
