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

3535

3232

4343

5858

4040

4040

3535

3232

4343

3434

5858

3535

5353

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

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

​$22000

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

​(c) Each employee in the sample takes a pay cut of

​$55000

from their original salary. Find the sample mean and the 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.

(Round to one decimal place as​ needed.)

### (a) Finding the Sample Mean and Sample Standard Deviation
Given the sample data (in thousands of dollars):
\[ 35, 32, 43, 58, 40, 40, 35, 32, 43, 34, 58, 35, 53 \]

1. **Sample Mean ($\bar{x}$):**
   The sample mean is calculated using the formula:
   \[
   \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
   \]
   where $x_i$ are the individual data points, and $n$ is the number of data points.

2. **Sample Standard Deviation ($s$):**
   The sample standard deviation is calculated using the formula:
   \[
   s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}
   \]

Let’s perform these calculations.The sample mean is approximately $ 41.4 $ thousand dollars, and the sample standard deviation is approximately $ 9.4 $ thousand dollars.

### (b) Each Employee Gets a $22,000 Raise
This implies adding 22 (in thousands) to each salary in the dataset. Let's calculate the new sample mean and sample standard deviation.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you would like to continue with the problem, you can provide the new instructions, and I can attempt to help further with a different approach. 

Here are some questions related to the problem for further exploration:
1. How would adding a constant value to every data point in a dataset affect the mean?
2. How does adding a constant value affect the standard deviation of a dataset?
3. What happens to the mean and standard deviation if every data point in the dataset is multiplied by a constant?
4. How does a decrease in salary affect the variance of a dataset?
5. How would removing an outlier affect the mean and standard deviation?

**Tip:** When adding or subtracting a constant to every data point in a dataset, only the mean changes, while the standard deviation remains the same.

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 35, 32, 43, 58, 40, 40, 35, 32, 43, 34, 58, 35, 53. (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a $22000 raise. Find the sample mean and sample standard deviation for the revised data set. (c) Each employee in the sample takes a pay cut of $55000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

This problem involves finding the sample mean and standard deviation for employee salaries at a company. The problem covers calculating statistical measures for the original data, then revising the calculations after a $22000 raise and a $55000 pay cut. Learn how to adjust the mean and standard deviation under different salary changes. Suitable for students in Grades 10-12.

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