Calculate the standard deviation of the data shown. Use technology

x
5.8
10.6
18.9
19.6
26

Round to 2 places.
Submit Question Question 11

To calculate the standard deviation of the given data set using technology, follow these steps:

1. **List the data**: 
   \( x = [5.8, 10.6, 18.9, 19.6, 26] \)

2. **Find the mean (\(\mu\))**:
   \[
   \mu = \frac{5.8 + 10.6 + 18.9 + 19.6 + 26}{5}
   \]
   
3. **Calculate the variance**:
   \[
   \text{Variance} = \frac{(x_1 - \mu)^2 + (x_2 - \mu)^2 + \ldots + (x_n - \mu)^2}{n}
   \]
   
4. **Take the square root of the variance to find the standard deviation**:
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Let me calculate that for you.The standard deviation of the given data set is **7.13** (rounded to two decimal places).

Would you like any details or have any questions about this calculation?

Here are five related questions to consider:

1. How is the standard deviation different from the variance?
2. What is the significance of using the population standard deviation instead of the sample standard deviation?
3. How would the standard deviation change if one of the data points was an outlier?
4. Can the standard deviation ever be negative? Why or why not?
5. How does standard deviation help in understanding the spread of data?

**Tip:** Standard deviation is most informative when comparing datasets with similar means; it tells you how much the data deviates from the mean on average.

Learn how to calculate the standard deviation of the data set [5.8, 10.6, 18.9, 19.6, 26] with a detailed step-by-step solution. This problem covers key statistical concepts, including mean calculation, variance computation, and standard deviation. Suitable for Grades 11-12.

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