The hardcover book was about 3/4" thick. The book is good fiction for teenagers and older preteens. I read the book in 1959 on a USN base in the Philippines, I believe the genius girl Violet was not over 12, probably in the range of 10 to 12 but possibly younger.
The only other details in the book that I remember are that some (maybe most) of the book was funny. Also, that Violet was in a Shakespeare school play and, without telling anyone, she rewrote her parts and the poor boy that was in the play was confused and probably frightened because he didn't recognize her parts. However, she ended her parts with the proper cues so the boy could say his parts. And, someone watching the play commented that Shakespeare seems different than she remembers.