“We needed her,” the family said. “The girls needed her. And she ended up being our rock through it all.”

To her daughter, she had long been a model for stability and support. In her memoir, “Becoming,” Mrs. Obama wrote that she had wanted to be both a career woman — her idol in that department was Mary Tyler Moore’s ambitious, eponymous TV character — and a “perfect” mother, like her own had been.

“I had so much — an education, a healthy sense of self, a deep arsenal of ambition,” Mrs. Obama wrote. “And I was wise enough to credit my mother, in particular, with instilling it in me.”

Marian Lois Shields Robinson was born on July 29, 1937, in Chicago. Her father, Purnell Shields, had moved to Chicago in the 1920s from Alabama to escape the Jim Crow South, and her mother, Rebecca Jumper, was a nursing aide. As a young woman, “she fell quickly and madly in love with Fraser Robinson, another South Sider with a boxer’s strength and jazz lover’s cool,” the family said. The Robinsons were married in 1960. Craig Robinson was born in 1962, and Michelle followed in 1964. Her husband, Fraser Robinson III, died in 1991.

The Robinsons raised their two children in a second-floor apartment on the South Side’s Euclid Avenue, where they interacted with a rotating cast of extended family members, including a great-aunt who taught piano and lived in the first-floor apartment. Mrs. Obama said that her mother and her other family members, including her protective older brother, shielded her from much of the tumult and civil rights protests that roiled Chicago and much of the nation in the late 1960s. Instead, the future first lady grew up peacefully, listening to the clinking of piano keys rising from the floor below.