Should one calculate annual average monthly salary or monthly gross salary to have a more accurate monthly salary an employee is receiving per annum? Is annual average monthly salary more accurate?

It can be seen as 4 components, of which the first one is the most important (for monthly average pay calculations) :

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Fair assumptions should be putting #2 to #4 as very optional (can be voided or not given in bad financial standings of a company).

1. Base pay (what you are taking home on a monthly basis, essential)
2. AWS (13th month bonus in other words) - Optional for companies
3. Performance Bonus - Optional for companies (very subjective)
4. Any other Bonuses - Eg. Corporate bonuses etc. (very very optional)

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Anything which is taxable i consider as "salary". which includes allowances, incentives, insurances.