Sometimes it is quite hard to decide which operator is better to use, especially when it comes to Average and Median. Of course, you always can use both of them  one metric to calculate the average and another the median. This will allow you to see which measure will be most useful in this particular case. However, understanding of this statistical terms will help you to make the right choice much faster.
Average (or mean) and median play the similar role in understanding the central tendency of a set of numbers. The average has traditionally been a popular measure of a middle point in a set, but it has a disadvantage of being influenced by single values which are much higher or lower than rest of the values. That’s why the median is a better midpoint measure for cases where a small number of outliers could drastically skew the average.
Average Median
Definition 
The average is the arithmetic mean of a set of numbers. 
The median is a numeric value that separates the higher half of a set from the lower half. 
When is it applicable? 
The mean is used for normal number distributions, which has the low amount of outliers. 
The median is generally used to return the central tendency for skewed number distributions. 
How to calculate? 
The average is computed by adding up all the values and dividing the sum by the total number of values. 
The median can be computed by listing all numbers in ascending order and then locating the number in the centre of that distribution. 
Example: Normal distribution 
2, 3, 3, 5, 8, 10, 11 (2+3+3+5+8+10+11)/7= 6 AVG = 6 
2, 3, 3, 5, 8, 10, 11
MEDIAN = 5 
Example: Skewed distribution 
2, 2, 3, 3, 5, 7, 8, 130 (2+2+3+3+5+7+8+130)/8= 20 AVG = 20 
2, 2, 3, 3, 5, 7, 8, 130 (3+5)/2=4 MEDIAN = 4 
Conclusion
If the data you are comparing is mostly uniform then you can safely use Average (AVG) operator. However, if your number set has some outliers then you need to consider using Median (MEDIAN) or to filter out values that are skewing the results.
Examples
Few practical examples:
 In order to report on Full Resolution time, I’ll use the default Full Resolution Time (hrs) [Mdn] metric. I’ll choose to use the median operator because I know that we have a number of tickets that are under investigation for a while and I don’t want this tickets skewing my report.
 If I want to check the average amount of Replies posted by the agents I’ll use # Replies [Avg] metric, because I know that the number of replies is more or less constant.
 If I need to figure out how fast the support team replies on new requests I can use the default First Reply Time (hrs) [Mdn] metric, but since I know that first reply time is normally constant I will choose to create a metric that will count average first reply time. Additionally, I will filter out proactive tickets, the once created by agents, from the report because most of them have irregularly high First reply time.
Here is a demo on how to transform a median metric into the average in Insights:
To transform a median metric into the average

Access an existing report or create a new one.

Find an average metric in Gooddata's What section.

With the metric highlighted, click View Detail.

Click Duplicate in the opened window, so as to keep the original metric untouched.

Rename the new metric to something appropriate, such as changing [MDN] to [AVG].

Click Edit, this will prompt you to the metric editor.

Highlight MEDIAN and type in AVG.

Click Save.

Use the new metric on your report.
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