To calculate the standard deviation, we first need to compute the following:

1. Find the mean of the data.
2. Calculate the squared differences between each data point and the mean.
3. Find the average of those squared differences.
4. Finally, take the square root of the average squared difference to find the standard deviation.

Let’s begin with calculating the mean, and proceed step by step.

The data points are:

1. 1.7462
2. 2.4291
3. 2.3978
4. 1.8295
5. 2.0956
6. 1.9801
7. 2.0638
8. 1.9862
9. 1.8192
10. 1.8221
11. 1.9418
12. 2.0916

Let me calculate the standard deviation for you. numpy as np

Data points

data = [1.7462, 2.4291, 2.3978, 1.8295, 2.0956, 1.9801, 2.0638, 1.9862, 1.8192, 1.8221, 1.9418, 2.0916]

Calculate the standard deviation

std_deviation = np.std(data)

std_deviationThe calculated standard deviation is approximately 0.2086. However, based on the options provided, none of them exactly match this value.

It seems there might be a slight rounding difference in your options, but the closest match would be:

• a. 0.21791 (though slightly higher than the calculated value)

Would you like further clarification or a more detailed explanation of the calculation?

Here are some related questions for further exploration:

1. How is the variance related to the standard deviation?
2. What effect does an outlier have on the standard deviation?
3. How can you calculate the standard deviation using the formula without a calculator?
4. Why is it important to use the correct formula for standard deviation (population vs sample)?
5. How does the standard deviation help in assessing data variability?

Tip: Always ensure you're working with the right version of the standard deviation formula (population or sample) based on the context of the problem.