Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed.

3939  

3232  

5252  

5353  

2929  

2929  

3939  

3232  

5252  

3535  

5353  

3939  

4848 
  
​(a) Find the sample mean and sample standard deviation.

​(b) Each employee in the sample is given a 

55​% 

raise. Find the sample mean and sample standard deviation for the revised data set.

​(c) To calculate the monthly​ salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set.

​(d) What can you conclude from the results of​ (a), (b), and​ (c)?

Question content area bottom

Part 1

​(a) The sample mean is 

x overbarxequals=enter your response here 

thousand dollars.

Let's break down the question into different parts and solve them step by step:

### Part (a): Find the sample mean and sample standard deviation.
The sample salaries (in thousands of dollars) are:
39, 32, 52, 53, 29, 29, 39, 32, 52, 35, 53, 39, 48.

#### Step 1: Sample Mean ( \( \bar{x} \) )
The formula for the sample mean is:
\[
\bar{x} = \frac{1}{n} \sum x_i
\]
where \( n \) is the number of data points, and \( x_i \) are the individual values in the data set.

#### Step 2: Sample Standard Deviation ( \( s \) )
The formula for the sample standard deviation is:
\[
s = \sqrt{\frac{1}{n-1} \sum (x_i - \bar{x})^2}
\]
Let me calculate the mean and standard deviation.

### Part (b): 55% Raise
If each employee gets a 55% raise, each salary will increase by a factor of 1.55. The new salaries are given by:
\[
\text{New salary} = \text{Old salary} \times 1.55
\]
We need to find the new mean and standard deviation after applying the raise.

### Part (c): Monthly Salaries
To calculate the monthly salary, each original salary is divided by 12. The new salaries will be:
\[
\text{Monthly salary} = \frac{\text{Old salary}}{12}
\]
We will find the new mean and standard deviation for the monthly salaries.

### Let's calculate these values now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Feel free to ask for any clarifications or provide additional questions.

Here are 5 relative questions based on this problem:
1. How do you interpret the sample standard deviation in this context?
2. What happens to the standard deviation if every salary is multiplied by a constant factor?
3. How does dividing each salary by a number (like 12 for monthly salary) affect the sample mean?
4. Can you predict what happens to the standard deviation when a constant amount is added to all data points?
5. How would you use this information to compare salary changes over time?

**Tip**: When calculating a raise or change in salary, always apply the percentage change to the original value first before making other adjustments (e.g., monthly calculation).

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 39, 32, 52, 53, 29, 29, 39, 32, 52, 35, 53, 39, 48. (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a 55% raise. Find the sample mean and sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

Learn how to calculate the sample mean and sample standard deviation for annual employee salaries, including adjustments for a 55% raise and conversion to monthly salaries. This problem covers essential statistics concepts such as sample mean, sample standard deviation, and data transformations. Suitable for students in Grades 10-12.

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