This formula represents the standard deviation of a population. It is expressed as:

$\sigma = \sqrt{\frac{\sum (x - \bar{x})^2}{n}}$

Here’s a breakdown of the components:

• $\sigma$ is the population standard deviation.
• $x$ represents each value in the data set.
• $\bar{x}$ is the mean (average) of the data set.
• $n$ is the total number of values in the population.
• $\sum (x - \bar{x})^2$ is the sum of the squared differences between each data point and the mean.

Explanation:

1. Step 1: Calculate the mean ($\bar{x}$) of the data set.
2. Step 2: Subtract the mean from each data point ($x - \bar{x}$) to find the deviation of each point.
3. Step 3: Square each deviation and then sum these squared values.
4. Step 4: Divide the sum of the squared deviations by the total number of data points ($n$).
5. Step 5: Take the square root of the result to obtain the standard deviation.

The standard deviation measures the amount of variation or dispersion in a set of data values.

Would you like a detailed example of how to calculate this, or any clarifications?

Here are 5 related questions to deepen your understanding:

1. How is the standard deviation different from the variance?
2. What is the difference between population standard deviation and sample standard deviation?
3. Can the standard deviation ever be negative?
4. Why do we square the deviations when calculating variance and standard deviation?
5. How does standard deviation help in understanding data spread?

Tip: When dealing with large data sets, using technology like calculators or software for these calculations can save time and avoid manual errors.