‘‘Average Waves in Unprotected Waters’’ begins at dawn on the day Bet Blevins, the main character, must place her intellectually disabled son, Arnold, into an institution. At nine years old, Arnold has become too challenging for Bet to handle. In their rundown, one-room apartment, Bet questions whether Arnold understands what is happening as she prepares his belongings and dresses him for the last time. She also wonders if she is truly making the right choice. As they leave their dilapidated building, Mrs. Puckett, a compassionate neighbor, stops Bet while crying and hands her cookies for Arnold. However, Arnold runs off without acknowledging the woman who has cared for him since he was born.

After taking a bus from their apartment, Bet and Arnold reach the train station. Bet has bought gum for a nervous Arnold. As the train departs, Arnold calms down and falls asleep. While he sleeps, Bet reminisces about Arnold as a younger child and recalls her husband, Avery, who left shortly after Arnold's condition was diagnosed. She concludes that they married too young, against her parents’ advice. She ponders whether Arnold's disability is due to Avery's genes or hers, suspecting it might be from her because ‘‘she never could do anything as well as most people.’’ She reflects on why she was so eager to leave her childhood home, now seeing it as ‘‘beautifully free and spacious.’’ She realizes that her enduring quality is her steadfastness. She remembers standing in the waves at the shore with her parents as a child, letting them crash over her, and draws a parallel to her life with Avery. After Avery left, she even stayed in the old apartment for a while because she ‘‘took some comfort from enduring.’’ When Arnold wakes up, she keeps him entertained, and they watch the conductor checking tickets. Arnold laughs at an old woman whom the conductor accuses of not having a ticket. Bet imagines herself in the old woman’s place, being reprimanded by the conductor.

Upon arriving in Parkinsville, Bet and Arnold take a cab to the Parkinsville State Hospital. Arnold asks for a cookie, but Bet refuses, worried he might get messy. She wants the hospital staff to see that ‘‘someone cherished him.’’ She fears Arnold might have one of his outbursts. To placate him, she breaks off a small piece of cookie for him to eat. At the hospital, she repeatedly asks the cab driver if he will wait for her, and he assures her that he will.

Inside the hospital, a nurse provides Bet with a tour, showing her where Arnold will be staying. As they walk around, Bet attempts to explain how Arnold should be cared for. The nurse reassures her that Arnold will receive excellent care and informs her that she won't be able to visit him for six months while he adjusts to his new environment. After leaving Arnold with his blanket, Bet says her goodbyes.

In tears, Bet quickly leaves the building, gets into a cab, and urges the driver to hurry to the train station. She has planned her departure to minimize her wait for the train. Upon arriving at the station, she discovers that the train has been delayed by twenty minutes. This news nearly drives her to desperation as she wonders how she will cope with the seemingly endless wait. Just then, the town’s mayor enters the station and announces that he will deliver a twenty-minute speech. Bet feels a sense of relief, believing that they have ‘‘come just for her sake,’’ and from now on, everything will be like that—‘‘just something on a stage, for her to sit back and watch.’’