The median and mode.
No they are not the same in a unimodal symmetrical distribution and they will never be
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).
for symmetrical distributions your mean equals the median. that is one of the properties of the symmetrical 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.
yes it is true
No they are not the same in a unimodal symmetrical distribution and they will never be
Your distribution is unimodal and symmetrical.
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).
Yes, and they WILL be if the distribution is symmetrical.
No. They are equal only if the distribution is symmetrical.
for symmetrical distributions your mean equals the median. that is one of the properties of the symmetrical distribution.
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.
No.
mean deviation is minimum
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 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.
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).