when is it appropriate to use arithmetic mean as opposed to median
The median is the "middle" number in a set of data or a sequence. If you have the sequence 2,3,4,5,6 4 would be the median.
It is then the [arithmetic] mean of the two number. The sam applies if you have 6 numbers. The median is the mean of the 3rd and 4th numbers (in order).
Median of the set = arithmetic mean of 8 and 9 = 8.5
It is not: it may be better in some circumstances. The arithmetic mean and median are totally useless if the data are categoric. Think about a class of pupils recording what their favourite movie is and - unless they all choose the same film - try and figure out what the arithmetic mean or median could mean! There are also situations - particularly with highly skewed data - where the median is a superior indicator of the central tendency compared with the mean. Having said that, the arithmetic mean has some very important statistical properties and it has been studied extensively so there is a lot of information about it. It is beyond the scope of this site but if you are really interested you might want to read about the Central Limit Theorem. Warning: it is basic university level stuff.
when is it appropriate to use arithmetic mean as opposed to median
The median is the "middle" number in a set of data or a sequence. If you have the sequence 2,3,4,5,6 4 would be the median.
The median of 25 and 50 is also their arithmetic mean. 37.5
As the mean is greater than the median it will be positively skewed (skewed to the right), and if the median is larger than the mean it will be negatively skewed (skewed to the left)
Of these three, the median is most resistant.
It is the same as the arithmetic mean of the two: 312.5
Median of the set = arithmetic mean of 75 and 85 = 80
mode
The median is defined as the middle value in a set or distribution. There is no arithmetic involved in finding the median unless the set or distribution has an even number of values, in which case the the two middle values (sometimes defined as lower median and upper median) are averaged to find the median.
It is then the [arithmetic] mean of the two number. The sam applies if you have 6 numbers. The median is the mean of the 3rd and 4th numbers (in order).
Median of the set = arithmetic mean of 8 and 9 = 8.5
If you have a list of positive and negative numbers then it is possible that the median would be 0.