The standard error (SE) is related to the standard deviation (SD) by the formula:
\[ \text{SE} = \frac{\text{SD}}{\sqrt{n}} \]
where \( n \) is the sample size. To find the standard deviation, we can rearrange the formula:
\[ \text{SD} = \text{SE} \times \sqrt{n} \]
Given that the standard error (SE) is 7.8 and the sample size (n) is 10, we can substitute these values into the equation:
\[ \text{SD} = 7.8 \times \sqrt{10} \]
Now, calculating \( \sqrt{10} \):
\[ \sqrt{10} \approx 3.1623 \]
Now, multiplying this by the standard error:
\[ \text{SD} = 7.8 \times 3.1623 \approx 24.693 \]
Now, rounding to the nearest hundredth:
\[ \text{SD} \approx 24.69 \]
Thus, the standard deviation is approximately 24.69.