Fifteen year-old Connie is a young girl going through the challenges of adolescence in 1960's suburbia. We get a few important details about her family from the narrative, but it is up to the reader to exercises their own analysis of what each character brings as part of a whole family.
At the very beginning of the story, we get a description of Connie's mother, as well as a description of their dynamics. Connie's mother is said to "know and notice everything", and is prone to criticizing Connie for the latter's penchant of looking at herself in the mirror.
We find out shortly after that Connie's mother is actually jealous of Connie, for she "hadn't much reason any longer to look at her own face". This suggests a type of immature relationship where the mother, rather than delineating her role, lowers her intellect to the emotional stage of her child and acts like a peer. This is typical of parents who have not claimed their role within the family.
Connie's mother nags a lot, judges a lot, and annoys Connie a lot. She compares Connie constantly to her (Connie's) much older sister, June. However, it seems as if the three women of the family simply cannot find a happy medium, as the story suggests that Connie's mom would
complained over the telephone about one sister to the other, and then the other called up and they would both complain about the third one.
This leads to the necessary description of June as Connie's foil.
June is in her twenties and, as the text suggests, she is bound to become a spinster for she still lives at home with her mother and sister, and still follows the same routines as when she was much younger. She is the "good sheep" of the family, as she does her best to please her mother. June is also unattractive and overweight. Apparently she is also very shy when compared to Connie, who easily goes out to look at boys with her friends from school. Hence June is simply existing in the home, as one more ornamental figure in Connie's life. Connie believes that her mother prefers her for being more attractive than June, but they still argue.
The father is described as a man who was at work all the time, and only cared about coming from work, getting his supper, and going to bed. He really did not socialize much with his family, and seems to have found nothing in common in a family where he is outnumbered and perhaps even overpowered. For this reason, the influence of Connie's father in her life is quite minimal.
The fact that this seems like a highly permissive parental unit suggests that Connie's family was trying to modernize their values and be more than the authoritarian parent of the previous decades. However, it is clear that their permissiveness, aloofness and lack of focus on the development of the family unit ultimately led Connie to her final fate.