Final answer:
Roger sits on the far side of the room in order to show Mrs. Jones that he is not taking anything from her purse.
Step-by-step explanation:
In the story 'Thank You, Mam,' Roger sits on the far side of the room when Mrs. Jones goes behind the screen because he wants her to see that he is not taking anything from her purse. When Mrs. Jones leaves her purse unattended, Roger has an opportunity to take money from it, but he chooses not to and instead sits on the far side of the room to show his honesty and earn Mrs. Jones' trust.