Calculate the Standard Deviation (to 4 decimal places) from the following list of values:
 
14.28, 13.89, 15.68, 12.29 ,17.46, 14.82, 13.89, 18.53, 17.62, 14.39, 17.64, 11.75, 15.96, 15.4, 17.4, 13.49, 14.71, 14.39, 19.81, 15.71, 16.23, 17.74, 15.4
 
Calculate the Standard Deviation (to 4 decimal places) from the following list of values:
 
14.28, 13.89, 15.68, 12.29 ,17.46, 14.82, 13.89, 18.53, 17.62, 14.39, 17.64, 11.75, 15.96, 15.4, 17.4, 13.49, 14.71, 14.39, 19.81, 15.71, 16.23, 17.74, 15.4
 



Let's calculate the standard deviation for the given list of values:

**Values:**
\[ 14.28, 13.89, 15.68, 12.29, 17.46, 14.82, 13.89, 18.53, 17.62, 14.39, 17.64, 11.75, 15.96, 15.4, 17.4, 13.49, 14.71, 14.39, 19.81, 15.71, 16.23, 17.74, 15.4 \]

### Steps to calculate standard deviation:
1. **Calculate the mean** of the data set.
2. **Subtract the mean** from each data point and square the result.
3. **Calculate the variance** by finding the average of these squared differences.
4. **Take the square root** of the variance to get the standard deviation.

Let's perform these calculations.The standard deviation of the given list of values is **1.9627** (rounded to four decimal places).

Would you like more details on the calculation process or have any other questions?

Here are 5 related questions to expand your understanding:
1. How does the standard deviation change with different sample sizes?
2. What does a low standard deviation indicate about the data set?
3. How is the standard deviation affected by outliers?
4. What is the difference between standard deviation and mean absolute deviation?
5. How can standard deviation be used in comparing two different data sets?

**Tip:** When comparing the spread of two data sets, standard deviation provides a good measure of how much variation exists within each set.

Learn how to calculate the standard deviation (to 4 decimal places) from a given list of values. Understand the steps involved, including calculating the mean, variance, and the final standard deviation. This problem involves statistical concepts and is suitable for college-level students or anyone interested in statistical analysis.

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