This is a good question, as the tone sets the whole mood of the movie, and it gives the viewer a preview of what to expect. That said, it should be pointed out that the movie was made in 1967. So, it is not too modern by our standards.
I would say that the movie has a serious tone. The topic is one that is important and the issues that it deals with are pressing for all generations (education and coming of age). Moreover, the situation is no laughing matter. Mr. Thackeray (the protagonist) is without a job and the kids are badly behaved (and their futures does not look good).
With this stated, it should also be stated that one tone does not necessary prohibit other tones. Therefore, there are funny scenes and other scenes as well.