simple, annual salaries and thousands of dollars for employees at a company are listed: 50 31 56 29 29 50 31 56 26 51 50 41 a) find a sample mean and sample standard deviation.b.) each employee in the sample is given a $5000 raise. Find the sample mean and sample standard deviation for the revised dataset.c.) each employee in the sample takes a pay cut of $2000 from the originals hour. Find a sample mean and sample standard deviation for the revised dataset.d.) **Educational Resource: Analyzing Sample Annual Salaries**Sample annual salaries (in thousands of dollars) for employees at a company are listed:50, 31, 56, 51, 29, 29, 50, 31, 56, 26, 51, 50, 41**Problems:**(a) Find the sample mean and sample standard deviation.(b) Each employee in the sample is given a $5000 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 $2000 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)?---**Solutions:**(a) The sample mean is $ \overline{x} = \boxed{42.4} $ thousand dollars. (Round to one decimal place as needed.)The sample standard deviation is $ s = \boxed{?} $ thousand dollars.(Round to one decimal place as needed.)(b) The sample mean is $ \overline{x} = \boxed{?} $ thousand dollars.(Round to one decimal place as needed.)The sample standard deviation is $ s = \boxed{?} $ thousand dollars.(Round to one decimal place as needed.)(c) The sample mean is $ \overline{x} = \boxed{?} $ thousand dollars.(d) **Conclusion:**What can you conclude from the results of (a), (b), and (c)?**Explanation:**In this exercise, you are tasked with calculating the sample mean and standard deviation for a given data set of employee salaries. You will then adjust these salaries with increases and decreases and recalculate to observe the changes. This helps in understanding the impact of uniform changes in data on statistical measures.**Attached Graph/Diagram Explanation:**The image contains a partial worked example showing the computation of the sample mean (average) of the given salaries. In part (a), the calculated mean is documented as 42.4 thousand dollars, but the sample standard deviation is not provided. Subsequent parts (b) and (c) involve adjusting the salaries by fixed amounts ($5000 raise and $2000 pay cut) and recalculating the mean and standard deviation. The calculations for these adjusted **Sample Annual Salaries Analysis**### Sample annual salaries (in thousands of dollars) for employees at a company are listed:50, 31, 56, 51, 29, 29, 50, 31, 56, 26, 51, 50, 41#### Tasks:**(a)** Find the sample mean and sample standard deviation.**(b)** Each employee in the sample is given a $5000 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 $2000 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)?---*(Round to one decimal place as needed.)*- The sample standard deviation is $ s $ = [blank] thousand dollars.*(Round to one decimal place as needed.)*---#### What can you conclude from the results of (a), (b), and (c)?Choose the correct answer:- **A.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the new sample standard deviation is $ s + k $. - **B.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the new sample standard deviation is $ s \cdot k $.- **C.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the sample standard deviation remains unaffected. - **D.** When a constant $ k $ is added to or subtracted from each entry, the sample mean is unaffected, and the new sample standard deviation is $ s + k $ or $ s - k $, respectively.---### Explanation:1. **Finding the Mean and Standard Deviation**: - To find the mean (average), add all the salary values together and divide by the total

For standard deviation:The standard deviation is a measure of "spread", i.e. how far values vary…

Answered: ← Sample annual salaries (in thousands…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

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Question

simple, annual salaries and thousands of dollars for employees at a company are listed:

50 31 56 29 29 50 31 56 26 51 50 41

a) find a sample mean and sample standard deviation.

b.) each employee in the sample is given a $5000 raise. Find the sample mean and sample standard deviation for the revised dataset.

c.) each employee in the sample takes a pay cut of $2000 from the originals hour. Find a sample mean and sample standard deviation for the revised dataset.

d.)

**Educational Resource: Analyzing Sample Annual Salaries**

Sample annual salaries (in thousands of dollars) for employees at a company are listed:
50, 31, 56, 51, 29, 29, 50, 31, 56, 26, 51, 50, 41

**Problems:**
(a) Find the sample mean and sample standard deviation.
(b) Each employee in the sample is given a $5000 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 $2000 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)?

---

**Solutions:**

(a) The sample mean is $ \overline{x} = \boxed{42.4} $ thousand dollars.
(Round to one decimal place as needed.)

The sample standard deviation is $ s = \boxed{?} $ thousand dollars.
(Round to one decimal place as needed.)

(b) The sample mean is $ \overline{x} = \boxed{?} $ thousand dollars.
(Round to one decimal place as needed.)

The sample standard deviation is $ s = \boxed{?} $ thousand dollars.
(Round to one decimal place as needed.)

(c) The sample mean is $ \overline{x} = \boxed{?} $ thousand dollars.

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

**Explanation:**
In this exercise, you are tasked with calculating the sample mean and standard deviation for a given data set of employee salaries. You will then adjust these salaries with increases and decreases and recalculate to observe the changes. This helps in understanding the impact of uniform changes in data on statistical measures.

**Attached Graph/Diagram Explanation:**

The image contains a partial worked example showing the computation of the sample mean (average) of the given salaries. In part (a), the calculated mean is documented as 42.4 thousand dollars, but the sample standard deviation is not provided. Subsequent parts (b) and (c) involve adjusting the salaries by fixed amounts ($5000 raise and $2000 pay cut) and recalculating the mean and standard deviation. The calculations for these adjusted

**Sample Annual Salaries Analysis**

### Sample annual salaries (in thousands of dollars) for employees at a company are listed:
50, 31, 56, 51, 29, 29, 50, 31, 56, 26, 51, 50, 41

#### Tasks:

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

**(b)** Each employee in the sample is given a $5000 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 $2000 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)?

---

*(Round to one decimal place as needed.)*

- The sample standard deviation is $ s $ = [blank] thousand dollars.

*(Round to one decimal place as needed.)*

---

#### What can you conclude from the results of (a), (b), and (c)?
Choose the correct answer:

- **A.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the new sample standard deviation is $ s + k $.

- **B.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the new sample standard deviation is $ s \cdot k $.

- **C.** When a constant $ k $ is added to or subtracted from each entry, the new sample mean is $ \bar{x} + k $ or $ \bar{x} - k $, respectively, and the sample standard deviation remains unaffected.

- **D.** When a constant $ k $ is added to or subtracted from each entry, the sample mean is unaffected, and the new sample standard deviation is $ s + k $ or $ s - k $, respectively.

---

### Explanation:

1. **Finding the Mean and Standard Deviation**:
- To find the mean (average), add all the salary values together and divide by the total

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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