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?

Answer 1

Let the Mean$=\frac{(3+4+5+5+8)}{5}=\frac{25}{5}=5$

Median$=5$

Mode$=5$ ($5$ has frequency $2$)

Four integers are added to a group of integers data increases by $1$ each therefore,

Mode$=6$

In group of integers $6$ must be $3$ times,therefore Let fourth integer$=x$

Group of integers$=3,4,5,5,6,6,6,8$ and $x$

Therefore new mean is $6$

$\frac{(3+4+5+5+6+6+6+8+x)}{9}=6$

Implies that

$\frac{(43+x)}{9}=6$

Implies that

$43+x=54$

$x=54-43$

$x=11$.