Question:
The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46, find the 6th number.
Solution:
Mean of 11 numbers $=42$
Sum of 11 numbers $=42 \times 11=462$
Mean of the first 6 numbers $=37$
Sum of the first 6 numbers $=37 \times 6=222$
Mean of the last 6 numbers $=46$
Sum of the last 6 numbers $=46 \times 6=276$
$\therefore 6$ th number $=[($ Sum of the first 6 numbers $+$ Sum of the last 6 numbers $)-$ Sum of 11 numbers $]$
$=[(222+276)-462]$
$=[498-462]$
$=36$
Hence, the 6 th number is 36 .
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