\begin{align*}
\text{Numerator = } & E[X^3] - 3 \mu E[X^2] + 2\mu^3\\
& = \left [ 0^3 \cdot 0.10 + 1^3 \cdot 0.25 + 2^3 \cdot 0.40 + 4^3 \cdot 0.15 + 7^3 \cdot 0.10 \right ] - 3 \cdot 2.35 \cdot 9.15 + 2 \cdot 2.35^3\\
& \approx 0 + 0.25 + 3.20 + 9.60 + 34.3 - 64.5075 + 25.96\\
& = 47.35 - 64.5075 + 25.96\\
& \approx 8.80
\end{align*}
which yields a skewness of \(\gamma_1 = 8.80 / \sigma^3 \approx 1.27 \text{.}\) This indicates a slight skewness to the right of the mean. You can notice the 4 and 7 entries on the histogram illustrate a slight trailing off to the right.