Create Multidimensional Inequality Index

I want to create an index to measure inequality in education. First of all, it would be necessary to identify the inequality within the 5 educational level. Therefore, I seperated 5 level to calculate index for each one of them. First, I will calculate the indicators and then the dimension index for that education (primary, secondary, etc.) category.
Finally, I will weight each educational category by the total number of individuals in the data set. Or I will compare the general indexes I have obtained with each other considering to educational categories.
My question is, would that be a statistically valid approach? My aim is to create a multidimensional education inequality index using the education level.
(Note: I will use the PCA method to determine indicator and dimensions. The table is for illustrative purposes only)
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