Question

Six numbers from a list of nine integers are $7$, $8$, $3$, $5$, $9$, and $5$. What is the largest possible value of the median of all nine numbers in this list

Answer 1

8  is the largest possible value of the median of all nine numbers in this list.

Lets simplify it,

⇒  The given six numbers are 7,8,3,5,9 and 5.

⇒  Arrange the six numbers in order 3,5,5,7,8,9.

⇒  We have three more numbers to insert into the list, and the median will be the  highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.

∴  The median is the 5th item of data which is 8.

∴  Median=8

Hence 8  is the largest possible value of the median of all nine numbers in this list.

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