Question

Four integers are added to a group of integers $3,4,5,5$ and $8$ and the mean, median, and mode of the data increases by $1$ each. What is the greatest integer in the new group of integers?

• A. $6$
• B. $11$
• C. $5$
• D. $13$

Answer 1

The correct option is B $11$

The given integers are $3,4,5,5,8$

$Mean=(3+4+5+5+8)\frac{25}{5}=5\therefore Median=5\&Mode=5$

after adding $4$ integers , mode is increased by $1$

Therefore the new $Mode$ is $6$.

$\because mode$ is frequently occurs value.

$\therefore$ $6$ must be added at least $3$ times.

$\therefore$ THe new set of integers will be $3,4,5,5,6,6,6,8$ & $X$

Let the $4^{th}$ integer be in ${}^{\prime }{X}^{\prime }$.

And new $Mean=6$

$6=\frac{(3+4+5+5+6+6+6+8+X)}{9}=>43+X=54=>X=54-43=>X=11$

So, greatest of $4$ integers next are added is $11$