The standard error (SE) is related to the standard deviation (SD) and the sample size (n) by the formula:
\[ SE = \frac{SD}{\sqrt{n}} \]
To find the standard deviation, we can rearrange this formula:
\[ SD = SE \times \sqrt{n} \]
Given that the standard error (SE) is 7.8 and the sample size (n) is 10, we can substitute these values into the equation:
\[ SD = 7.8 \times \sqrt{10} \]
Calculating \(\sqrt{10}\):
\[ \sqrt{10} \approx 3.162 \]
Now, we can calculate the standard deviation:
\[ SD = 7.8 \times 3.162 \approx 24.67 \]
Rounding to the nearest hundredth, the standard deviation is:
\[ \boxed{24.67} \]