To find the sample mean for the number of years worked and the percentage of employees who worked for the company for at least 10 years, follow these steps:
1. List of Values (Number of Years Worked):
The given data is:
[tex]\[
[3, 13, 28, 4, 12, 4, 26, 29, 3, 10, 3, 17, 13, 15, 15, 23, 13]
\][/tex]
2. Calculate the Sample Mean:
To find the sample mean (average) of years worked, sum all the values and divide by the number of values.
[tex]\[
\text{Sum of values} = 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13
\][/tex]
[tex]\[
\text{Number of values} = 17
\][/tex]
[tex]\[
\text{Sample mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\][/tex]
3. Calculate the Percentage of Employees Worked for at Least 10 Years:
To find the percentage of employees who worked for at least 10 years, count how many of the values are 10 or greater and divide by the total number of values, then multiply by 100 to get the percentage.
[tex]\[
\text{Number of employees with } \geq 10 \text{ years} = \text{Count of values} \geq 10
\][/tex]
[tex]\[
\text{Total number of employees} = 17
\][/tex]
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of employees with } \geq 10 \text{ years}}{\text{Total number of employees}} \right) \times 100
\][/tex]
After performing these calculations, we find:
- The sample mean for the number of years worked is 14.
- The percentage of employees who worked for at least 10 years is 71%.
Thus, the final answers are:
The sample mean for the number of years worked is 14, and 71% of the employees in the sample worked for the company for at least 10 years.
