Kingfish writes:

Chapter tests count for 60% of the final grade. Mid-term and final
tests count for 40% of the final grade. Scores for chapter tests were
80, 50 and 69. Mid-term and final tests were 80 and 90. What is the
final grade. One of us says 73.8 and the other says 80.7

The problem is incompletely specified (method of averaging not given)
and there are many "correct" answers.

By weighting the separate averages:

(80+50+69)*0.60/3 + (80+90)*0.40/2 = 73.8

But because the number of samples (3 and 2) happen to match the 60/40
weights, this is simply to overall average:

(80+50+69+80+90)/5 = 73.8

It would also be reasonable to use RMS averaging (75.0 here), or
different weights to the extreme score values (e.g., drop the lowest,
giving it a weight of zero). These would yield different result which
were less sensitive to sampling errors (one poor performance on a bad
day). But that's asking a lot from a shop teacher, I suppose.

All of which just shows that grades are full of noise and bias, and are
unreliable detectors of intelligence.