No they are not the same in a unimodal symmetrical distribution and they will never be
The median and mode.
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.
A normal distribution is symmetrical; the mean, median and mode are all the same, on the line of symmetry (middle) of the graph.
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 median and mode.
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).
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.
Yes, and they WILL be if the distribution is symmetrical.
No. They are equal only if the distribution is symmetrical.
A normal distribution is symmetrical; the mean, median and mode are all the same, on the line of symmetry (middle) of the graph.
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.
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.
First, I will give an example, similar to your question: -11000 -9000 +44000 mean = 8,000 and median = -9000. Symmetrical distributions after infinite sampling will show no difference in mean and median. Large differences are possible with small sample sizes even with symmetrical distributions. If the sample is large and the difference is large, this infers that the distribution is asymmetrical. The skewness of the distribution can be calculated.