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Kiera is writing a cookbook of bread recipes. For a section on different kinds of flour, she is making a chart listing the weight, in grams, of a cup each of $12$ different types of flour. The cups of flour all weigh between $85$ and $156$ grams, with $4$ of the types weighing $120$ grams. The mean of the weights of a cup of flour is about $116$ grams, and the mean absolute deviation is about $12.5$ grams.$\newline$Which is a typical weight of $1$ cup of flour?$\newline$(A) $12.5$ grams$\newline$(B) $116$ grams$\newline$(C) $120$ grams$\newline$(D) $156$ grams