To calculate the sample standard deviation for the given data, we follow these steps:

Step 1: Find the sample mean.

The data points are: $1, 6, 5$.

$\text{Mean} (\bar{x}) = \frac{1 + 6 + 5}{3} = \frac{12}{3} = 4$

Step 2: Calculate the squared differences from the mean.

Now, we subtract the mean from each data point and square the result:

$(1 - 4)^2 = (-3)^2 = 9$ $(6 - 4)^2 = (2)^2 = 4$ $(5 - 4)^2 = (1)^2 = 1$

Step 3: Find the sum of squared differences.

Add the squared differences:

$9 + 4 + 1 = 14$

Step 4: Divide by $n-1$ to get the variance.

Since this is a sample, we divide by $n-1 = 3-1 = 2$:

$\text{Variance} = \frac{14}{2} = 7$

Step 5: Take the square root to get the sample standard deviation.

$\text{Standard deviation} = \sqrt{7} \approx 2.6$

So, the sample standard deviation is 2.6.

Would you like details on how to proceed to the next steps or any clarifications?

Here are five related questions:

1. How is the sample standard deviation different from population standard deviation?
2. Why do we divide by $n-1$ for sample variance instead of $n$?
3. What assumptions are necessary for constructing a confidence interval?
4. How does increasing the confidence level affect the interval width?
5. What are the implications of having a small sample size on the confidence interval?

Tip: Always round your final answer according to the problem’s instructions, but keep more decimal places during intermediate steps for accuracy.