MS_Kekas wrote: You are given \( 11 \) numbers with an arithmetic mean of \( 10 \). Each of the first \( 4 \) numbers is increased by \( 20 \), and each of the last \( 7 \) numbers is decreased by \( 24 \). What is the arithmetic mean of the new \( 11 \) numbers? The sum of the old numbers is $11\cdot10=110$. After the modifications, this sum will increase by $20\cdot4-7\cdot24=-88$, hence a new sum of $110-88=22$. Therefore the new average is $\frac{22}{11}=\boxed2$.