One of the most endearing pieces of evidence that stands as a testament to Scout's new maturity is her treatment of Boo Radley. She greatly evolves in this regard from the beginning of the novel to the end.
Consider Scout's assessment of her neighbor in the first chapter:
Boo was about six-and-a-half feet tall, judging from his tracks; he dined on raw squirrels and any cats he could catch, that’s why his hands were bloodstained—if you ate an animal raw, you could never wash the blood off. There was a long jagged scar that ran across his face; what teeth he had were yellow and rotten; his eyes popped, and he drooled most of the time.
Early in the novel, Scout considers Boo more monster than human. She, Jem, and Dill spend time inventing stories about him. Their stories are fed when they listen to Miss Stephanie's gossip about how Boo sneaks around peeking in her window at night. They invent games to try to get him to emerge from his house; not once do they stop to consider his humanity.
By the end of the novel, Scout has gained wisdom about how all people should be treated. She learns to extend that kindness to Boo. Perhaps the most touching gesture of the story is when she needs to take Boo Radley home. She considers the delicate nature of their unique situation and then rises to the occasion with great insight:
"Will you take me home?"
He almost whispered it, in the voice of a child afraid of the dark.
I put my foot on the top step and stopped. I would lead him through our house, but I would never lead him home.
"Mr. Arthur, bend your arm down here, like that. That's right, sir."
I slipped my hand into the crook of his arm.
He had to stoop a little to accommodate me, but if Miss Stephanie Crawford was watching from her upstairs window, she would see Arthur Radley escorting me down the sidewalk, as any gentleman would do.
Scout knows the town is watching and makes an intentional effort to allow Arthur, who she no longer calls "Boo," to lead her. This allows him the respect of being a grown man, not someone who is led home by a young girl. This reflects a tremendous growth in Scout's ability to recognize the needs of others around her. She can empathize with the sensitive situation Arthur is in. He is completely exposed and vulnerable for the first time in many years.
She allows him the courteous titles of "mister" and "sir," as she would for any other adult, which stands in sharp contrast to her early days of dreaming up monster-like features. Scout's perception of Arthur Radley shows her new and more mature understandings of those who exist outside her immediate circle of experience.