The average of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured an average score of $80$ and the dullest $25\%$ secured an average score of $31$. Then the average score of remaining $55\%$ is:

Assume there are 100 students in total, so the overall sum of their scores is 100 times 52, which is 5200. The brightest 20 students have a sum of 20 times 80, equaling 1600, and the dullest 25 students have a sum of 25 times 31, equaling 775. The remaining 55 students have a score sum of 5200 minus 1600 minus 775, resulting in 2825, so dividing this by 55 gives an average score of approximately 51.4.

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