The Sample Mean For The Number Of Years Worked Is $\square$, And $\square$\% Of The Employees In The Sample Worked For The Company For At Least 10 Years. Round Your Answers To The Nearest Integer.\begin{tabular}{|c|c|}\hline Years
Introduction
In statistics, the sample mean is a measure of the central tendency of a dataset. It represents the average value of a variable in a sample of data. In this article, we will discuss how to calculate the sample mean for the number of years worked by employees in a company.
Calculating the Sample Mean
To calculate the sample mean, we need to add up all the values in the dataset and divide by the number of values. In this case, we have the following dataset:
Years | Frequency |
---|---|
1 | 10 |
2 | 15 |
3 | 20 |
4 | 25 |
5 | 30 |
6 | 35 |
7 | 40 |
8 | 45 |
9 | 50 |
10+ | 55 |
Step 1: Calculate the Sum of the Years
To calculate the sum of the years, we need to multiply each value by its frequency and add them up.
Years | Frequency | Years x Frequency |
---|---|---|
1 | 10 | 10 |
2 | 15 | 30 |
3 | 20 | 60 |
4 | 25 | 100 |
5 | 30 | 150 |
6 | 35 | 210 |
7 | 40 | 280 |
8 | 45 | 360 |
9 | 50 | 450 |
10+ | 55 | 550 |
The sum of the years is 2,229.
Step 2: Calculate the Sample Mean
To calculate the sample mean, we need to divide the sum of the years by the total number of employees.
Total number of employees = 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 = 325
Sample mean = Sum of the years / Total number of employees = 2,229 / 325 = 6.86
Rounding the Sample Mean
We are asked to round the sample mean to the nearest integer. Therefore, the sample mean is approximately 7 years.
Calculating the Percentage of Employees Who Worked for at Least 10 Years
To calculate the percentage of employees who worked for at least 10 years, we need to divide the number of employees who worked for 10 years or more by the total number of employees and multiply by 100.
Number of employees who worked for 10 years or more = 55
Percentage of employees who worked for at least 10 years = (55 / 325) x 100 = 16.92%
Rounding the Percentage
We are asked to round the percentage to the nearest integer. Therefore, the percentage of employees who worked for at least 10 years is approximately 17%.
Conclusion
Q: What is the sample mean, and why is it important?
A: The sample mean is a measure of the central tendency of a dataset. It represents the average value of a variable in a sample of data. The sample mean is important because it helps us understand the typical value of a variable in a population.
Q: How do I calculate the sample mean?
A: To calculate the sample mean, you need to add up all the values in the dataset and divide by the number of values. You can use the formula: Sample mean = (Sum of the values) / (Number of values).
Q: What is the difference between the sample mean and the population mean?
A: The sample mean is an estimate of the population mean. It is calculated from a sample of data, whereas the population mean is calculated from the entire population.
Q: How do I calculate the percentage of employees who worked for at least 10 years?
A: To calculate the percentage of employees who worked for at least 10 years, you need to divide the number of employees who worked for 10 years or more by the total number of employees and multiply by 100.
Q: What is the significance of the percentage of employees who worked for at least 10 years?
A: The percentage of employees who worked for at least 10 years is significant because it indicates the level of job satisfaction and commitment among employees. A high percentage may indicate that employees are happy with their job and are likely to stay with the company for a long time.
Q: How do I interpret the sample mean and the percentage of employees who worked for at least 10 years?
A: To interpret the sample mean and the percentage of employees who worked for at least 10 years, you need to consider the context of the data. For example, if the sample mean is high, it may indicate that employees are working long hours or are under a lot of stress. On the other hand, if the percentage of employees who worked for at least 10 years is high, it may indicate that employees are happy with their job and are likely to stay with the company for a long time.
Q: What are some common mistakes to avoid when calculating the sample mean and the percentage of employees who worked for at least 10 years?
A: Some common mistakes to avoid when calculating the sample mean and the percentage of employees who worked for at least 10 years include:
- Not rounding the sample mean to the nearest integer
- Not considering the context of the data when interpreting the results
- Not using the correct formula to calculate the sample mean and the percentage of employees who worked for at least 10 years
Q: How can I use the sample mean and the percentage of employees who worked for at least 10 years in real-world applications?
A: The sample mean and the percentage of employees who worked for at least 10 years can be used in real-world applications such as:
- Human resource management: to understand employee satisfaction and commitment
- Business planning: to make informed decisions about employee retention and recruitment
- Research: to study the effects of different variables on employee behavior and outcomes
Q: What are some limitations of the sample mean and the percentage of employees who worked for at least 10 years?
A: Some limitations of the sample mean and the percentage of employees who worked for at least 10 years include:
- They may not be representative of the entire population
- They may be affected by sampling errors
- They may not capture the nuances of employee behavior and outcomes
Conclusion
In this article, we have discussed some frequently asked questions about the sample mean and the percentage of employees who worked for at least 10 years. We have also highlighted some common mistakes to avoid and some real-world applications of these measures.