## **Core Concept**
The standard error (SE) of the mean is a statistical measure that estimates the variability of the sample mean. It is calculated as the standard deviation (σ) divided by the square root of the sample size (n). In this context, it's essential to understand the formula for standard error and its application in estimating population parameters.

## **Why the Correct Answer is Right**
The formula for standard error (SE) is (SE = frac{sigma}{sqrt{n}}), where (sigma) is the standard deviation and (n) is the sample size. Given that the standard deviation ((sigma)) is 1 gm% and the sample size ((n)) is 100, we can substitute these values into the formula: (SE = frac{1}{sqrt{100}} = frac{1}{10} = 0.1) gm%. Therefore, the standard error is 0.1 gm%, which corresponds to option .

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because it does not match the calculation of standard error using the given standard deviation and sample size.
- **Option B:** This option is incorrect for the same reason as option A; it doesn't align with the calculated standard error.
- **Option D:** This option suggests a standard error of 1, which would only be correct if the sample size were 1 (making the denominator of the SE formula equal to 1), but the sample size given is 100.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that as the sample size increases, the standard error decreases. This relationship highlights the importance of larger sample sizes in achieving more precise estimates of population parameters. In clinical research and practice, understanding the standard error helps in interpreting the reliability of sample data.

## **Correct Answer:** . 0.1 gm%