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I wouldn't say that the energy of a hybridized orbital is the average of its contributing orbitals. Instead, I like to think about how much each orbital contributed to the hybridized orbital's energy. For example, a sp^3 orbital has 25% s-character and 75% p-character. It would make sense that the hybridized orbital's energy will be much closer to the p-orbital in energy than an average would make it because the p-orbital makes up most of its energy.
Hybrid orbitals occur because we want to essentially form more bonds. For instance, a Carbon atom, by theory, says we can form 4 bonds because we have 4 valence electrons. However, when we take a look at the electron configuration, we can see that 2 of its electrons (in the s-orbital are already paired), suggesting that it can only for 2 bonds with its 2 unpaired electrons in the p-orbital. We know that this is not true, so instead hybridization occurs to combine the orbitals to allow more bonds to form. Thus, we can 4 sp3 orbitals, allowing for 4 bonds.
I would say it is an average of the other energies. This is seen by the ideas of s character and p character. The more p character it has, the closer it will be to the p orbitals and the farther it will be from the s orbitals.
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