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What is the relationship amount the mean median and mode in a symmetric disribution?
In a symmetric distribution, the mean, median, and mode are all equal or located at the same central point. This characteristic ensures that the distribution is balanced on either side, with half of the data points falling below the central value and half above it. Therefore, in a perfectly symmetric distribution, such as a normal distribution, these three measures of central tendency coincide.
What else can I help you with?
Can mean and median have one value?
Yes. And in any symmetric distribution, they will.
Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.
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.
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.
Is the mean always equal to the median for a normal distribution?
Yes, in a normal distribution, the mean is always equal to the median. This is because the normal distribution is symmetric around its mean, meaning that the values are evenly distributed on both sides. As a result, the central tendency measured by both the mean and the median coincides at the same point.
What is the relationship among the mean median and the mode in a symmetric distribution?
All equal.
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.
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.)
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.
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.
Normal distribution is symmetric about mean or median or mode?
Mean
Is the uniform probability distribution is symmetric about the mean and median?
yes
Can mean and median have same values?
Yes, they can.Yes, they can. In a symmetric distribution they will be the same.
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 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 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).
