To calculate the standard deviation for the given data set:

$x = \{22, 20, 3, 14, 15\}$

Steps:

1. Find the mean ($\bar{x}$): $\bar{x} = \frac{\sum x}{n}$

2. Find each deviation from the mean and square it: $(x_i - \bar{x})^2$

3. Calculate the variance ($s^2$) for a sample: $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$

4. Compute the standard deviation: $s = \sqrt{s^2}$

I will now compute this step-by-step. numpy as np

Given data

data = np.array([22, 20, 3, 14, 15])

Compute sample standard deviation (using n-1 in the denominator)

std_dev = np.std(data, ddof=1)

Round to one decimal place

std_dev_rounded = round(std_dev, 1) std_dev_roundedThe standard deviation of the given data set is 7.4 (rounded to one decimal place).

Would you like a detailed breakdown of the calculations?

Related Questions:

1. How is standard deviation different from variance?
2. What is the difference between population and sample standard deviation?
3. When should you use standard deviation in data analysis?
4. How does adding more data points affect standard deviation?
5. What are some real-world applications of standard deviation?

Tip: A higher standard deviation means the data points are more spread out from the mean.