To calculate the standard deviation of the sample data shown in the image, we’ll need to follow these steps:

1. Find the Mean (Average)

Calculate the mean ($\bar{x}$) of the sample data. This is the sum of all values divided by the number of values.

$\bar{x} = \frac{\sum x_i}{n}$

2. Calculate the Variance

For each data point ($x_i$), subtract the mean, square the result, and then average these squared differences. Since this is sample data, we’ll divide by $n - 1$, where $n$ is the number of data points.

$s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$

3. Take the Square Root

The sample standard deviation $s$ is the square root of the variance.

$s = \sqrt{s^2}$

I will go through each step if you provide the exact values in the sample data or confirm if you’d like me to read them directly from the image.

Would you like further guidance on any of these steps?

Here are some related questions to deepen understanding:

1. What is the difference between population and sample standard deviation?
2. How does changing a data value affect the standard deviation?
3. What are real-world scenarios where standard deviation is essential?
4. How does standard deviation relate to the concept of variance?
5. Why is $n-1$ used instead of $n$ when calculating sample variance?

Tip: When calculating standard deviation manually, double-check each step to ensure accuracy, especially with the mean and squared differences.