What is the relationship between Root Mean Square Deviation (s) and Standard Deviation `(sigma)`.

Answer

To find the relationship between Root Mean Square Deviation (s) and Standard Deviation (σ), we can follow these steps:

### Step 1: Define the terms
- **Standard Deviation (σ)**: It is a measure of the amount of variation or dispersion in a set of values.
- **Root Mean Square Deviation (s)**: It is another measure of the spread of a set of values, calculated as the square root of the average of the squares of the deviations from the mean.

### Step 2: Establish the relationship
We can express the relationship between Root Mean Square Deviation (s) and Standard Deviation (σ) mathematically. The relationship is given by the formula:

\[ s^2 = \sigma^2 + D^2 \]

Where:
- \( s \) = Root Mean Square Deviation
- \( \sigma \) = Standard Deviation
- \( D \) = Deviation from the assumed mean

### Step 3: Understand the components
- The term \( D \) represents the deviation of each data point from an assumed mean. This is important because the Root Mean Square Deviation takes into account the deviations from a mean that may not be the actual mean of the data set.

### Step 4: Conclusion
Thus, the relationship can be summarized as:

\[ s^2 = \sigma^2 + D^2 \]

This means that the square of the Root Mean Square Deviation is equal to the square of the Standard Deviation plus the square of the deviation from the assumed mean.

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