My school had valedictorian and salutatorian, but I really wish it didn't. The salutatorian cheated her way through school. I had gone to school with her from 7-12th grade and she had been accused of cheating many, many times, but the teachers never believed it. I remember she sat next to me in chemistry in high school. During a test, she had the chemistry book open next to her and was flipping through the pages to find the answers. The person who sat in front of me noticed it, and went to tell our teacher. He walked over to the girl, asked her why the chemistry book was open, and she responded, "Oh, it was like that when I sat down." The teacher then walked away totally accepting her response

. She ended up making a 100 on the test and the teacher refused to accept the fact that she cheated.
That very same year she was also in my AP English class and got caught cheating on a test. I think it was a vocabulary test (or something like that; can't quite remember) and she had put the list of words on the empty desk in front of her. The teacher walked around the classroom and saw the list. She questioned the girl if she had put the list there, and the girl said no. When the teacher turned around to go back to her desk, the girl turned to a friend, gave her a high-five, and said, "Whew. Glad I didn't get caught." After class let out, my friend went to tell the teacher that the list was, in fact, the girl's, but the teacher didn't believe her.
The teachers never believed she was the one actually cheating because she "looked so innocent and was too smart to cheat." Uh, yeah, ok
As for the valedictorian, she never cheated, but her speech at graduation was the most boring thing ever. She literally talked about her grandmother for 15 minutes. Sounds sweet, but it got
really old after 5 minutes. She literally started off her speech by finding her grandma in the audience, turning to her, and saying, "Oh grandma. I love you so much. You're such an inspiration to me. Remember that one time on vacation when we...." She only spoke to her grandma for the whole speech and didn't even address the graduating class at all. It was sweet, but was a bit strange, and quite boring.
Similar situation in our school. I don't know the criteria for NHS in our school, but the #3 student was not in it. It kind of boggled my mind. Geesh. I know, I know, maybe she did not participate in any other ativities, but I don't think some of the other kids, who did make it, were very involved either. This girl was not a trouble maker or anything like that. She won several scholarships on honors night, but she was not inducted into the honor society.
And, I'm still bitter about my own experience with the NHS 40 years ago. I was in the top ten, participated in several clubs and organizations, and was a commended PSAT student. I wasn't in the National Honor Society. Why? Apparently the advisor mostly nominated her own students.
NHS was similar in our school. A girl who graduated #5 in our class (of 490) was never invited to join NHS. She was in 5 different clubs at school (and was very involved in them), obviously had a high GPA, but was never invited to join.
All I remember about qualifying for NHS at my school was that you had to have above a 90% average. I was invited to join NHS, but didn't turn in my paperwork because I knew how much of a joke it was at my school.