First, let's calculate the mean of the given set.
The mean is given by the sum of all numbers divided by the amount of numbers:
[tex]\begin{gathered} mean=\frac{122+130+145+154+165+178}{6}\\ \\ mean=\frac{894}{6}\\ \\ mean=149 \end{gathered}[/tex]In order to increase the mean, we need to add a number that is greater than the mean.
Looking at the options, the only number that is greater than the mean is 150.
Therefore the correct option is D.
