Answer
The removed score:
$X=23$
Work Step by Step
$µ=\frac{∑X}{N}$
Before:
There are 8 scores whose mean is $16$:
$16=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8}{8}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8=16\times8=128$
One of the scores is removed. Since, the position of this score in the sum above makes no difference, let's name this score as $X_8$
After:
There are 7 scores whose mean is $15$:
$15=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7}{7}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7=15\times7=105$
But,
$X_1+X_2+X_3+X_4+X_5+X_6+X_7=(X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8)-X_8$
$105=128-X_8$
$X_8=128-105$
$X_8=23$
