Standard Deviation P and Standard Deviation S - SD

In Power BI, Standard Deviation P and Standard Deviation S refer to two different methods for calculating standard deviation, and they differ in the way they handle sample data versus population data. Here’s an overview of each:

1. Standard Deviation P (Population Standard Deviation)

• Formula:

  $$\sigma = \sqrt{\frac{\sum{(X_i - \mu)^2}}{N}}$$

• where:

  • $X_i$ = Each data point

  • $\mu$ = Population mean

  • $N$ = Total number of data points (in the entire population)

• Purpose: Used when you have data for the entire population. The denominator uses $N$ (the total number of data points).

• When to Use:

  • Use Standard Deviation P when the data set represents the entire population or when you know that you have data for every single element in the population (for example, all employees in a company, all customers in a region).

• Application in Data Analytics:

  • Ideal for analyzing complete datasets where you’re looking to measure variability or dispersion within the entire population.

2. Standard Deviation S (Sample Standard Deviation)

• Formula:

  $$s = \sqrt{\frac{\sum{(X_i - \bar{X})^2}}{n-1}}$$

  where:

  • $X_i$ = Each data point

  • $\bar{X}$ = Sample mean

  • $n$ = Number of data points (sample size)

• Purpose: Used when you're working with a sample from a larger population. The denominator uses $n - 1$, which corrects the bias in the estimation of the population's standard deviation from a sample.

• When to Use:

  • Use Standard Deviation S when your data represents a sample from a larger population and you are estimating the population’s standard deviation from that sample (e.g., when analyzing survey data or a random sample of customers).

• Application in Data Analytics:

  • Ideal when the dataset you’re analyzing is a subset or a sample of a larger group, and you're making inferences about the population as a whole based on the sample data.

Key Differences:

• Population vs Sample:

  • Standard Deviation P is used for the entire population, while Standard Deviation S is used when dealing with a sample.

• Formula Adjustment:

  • The Standard Deviation S formula adjusts for bias by dividing by $n-1$, whereas Standard Deviation P divides by $N$.

When to Use Each in Power BI:

• Standard Deviation P:

  • Use when you're confident that your dataset represents the entire population (e.g., analyzing all transactions of a company).

  • Example: You might use this when evaluating the total revenue generated by all branches of a company.

• Standard Deviation S:

  • Use when your dataset is a sample from a larger group (e.g., survey data, random samples from a large customer base).

  • Example: Analyzing customer satisfaction scores from a sample of respondents rather than all customers.

Applications in Data Analytics:

• Population Standard Deviation (P):

  • Helps understand how data points in the full population deviate from the mean, which is crucial in quality control, risk analysis, and large-scale market research.

• Sample Standard Deviation (S):

  • Used to estimate the variability in a larger population based on a sample. It's widely used in statistical hypothesis testing, regression analysis, and predictive modeling, particularly when you don't have access to complete data.

In summary, the choice between Standard Deviation P and Standard Deviation S in Power BI depends on whether you're working with a complete population or a sample from a larger population.