A random sample of 50 employees from a large company has an average monthly income of K2,000 with a standard deviation of K400.

1)	What is the standard error of the mean? 


The **standard error of the mean (SEM)** is a measure of how much the sample mean is expected to fluctuate from the true population mean. It is calculated using the formula:

\[
\text{SEM} = \frac{s}{\sqrt{n}}
\]

Where:
- \( s \) is the sample standard deviation
- \( n \) is the sample size

For this problem:
- \( s = K400 \)
- \( n = 50 \)

Now, we calculate the standard error:

\[
\text{SEM} = \frac{400}{\sqrt{50}} \approx \frac{400}{7.071} \approx 56.57
\]

So, the **standard error of the mean** is approximately **K56.57**.

Would you like more details on this calculation or further explanation?

Here are 5 related questions you might find helpful:
1. How does increasing the sample size affect the standard error?
2. What is the relationship between standard deviation and standard error?
3. How would the standard error change if the sample size was doubled?
4. What does a smaller standard error indicate about a sample?
5. How can we use the standard error to construct confidence intervals?

**Tip:** The standard error decreases as the sample size increases, indicating more precise estimates of the population mean.

A random sample of 50 employees from a large company has an average monthly income of K2,000 with a standard deviation of K400. 1) What is the standard error of the mean?

Learn how to calculate the standard error of the mean for a sample of 50 employees with a given standard deviation of K400. This problem involves key statistical concepts such as standard error and sample size, and is suitable for students in Grades 10-12.

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