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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).

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Q: In a perfectly symmetrical unimodal distribution is the mode and the median the same as the mean?
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Related questions

Are the mean median and the mode the same in a unimodal symmetrical distribution?

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


In a unimodal symmetrical distribution the mean is equal to?

The median and mode.


What would be the implications if the mean mode and median were equivalent?

Your distribution is unimodal and symmetrical.


In a perfectly symmetrical bell-shaped normal distribution?

Normal distribution is a perfectly symmetrical bell-shaped normal distribution. The bell curve is used to find the median, mean and mode of a function.


The mean of a symmetrical distribution is 40What is its median?

for symmetrical distributions your mean equals the median. that is one of the properties of the symmetrical distribution.


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.


Can the mean be equal to the median?

Yes, and they WILL be if the distribution is symmetrical.


Does mode equals the median normal distribution?

Yes it is. The normal distribution is symmetrical around the mode. Therefore the median has to be the same :)


Are the mean and the median always equal?

No. They are equal only if the distribution is symmetrical.


How does the median affect the graph of a normal distribution?

A normal distribution is symmetrical; the mean, median and mode are all the same, on the line of symmetry (middle) of the graph.


Is the mean and median similar?

The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.


What is the nature of symmetry if median is greater than the mean?

Generally, when the median is greater than the mean it is because the distribution is skewed to the left. This results in outliers or values further below the median than above the median which results in a lower mean value than median value. When a distribution is skewed left, it is generally not very symmetrical or normally distributed.