Question

Find the standard deviation of salaries of each department in descending order?

Answer 1

To find the standard deviation of salaries of each department in descending order, calculate the standard deviation for each department and arrange them in descending order based on their standard deviations. Collect the salaries data for each department, calculate the mean salary for each department, calculate squared differences, find the variance, and calculate the standard deviation. Arrange the standard deviations in descending order to find the department with the highest standard deviation.

Step-by-step explanation:

To find the standard deviation of salaries of each department in descending order, you would first calculate the standard deviation for each department and then arrange them in descending order based on their standard deviations. Here's how you can do it:

1. Collect the salaries data for each department.
2. Calculate the mean (average) salary for each department.
3. Calculate the squared differences between each salary and the mean salary for each department.
4. Calculate the variance by finding the average of the squared differences for each department.
5. Take the square root of the variance to get the standard deviation for each department.
6. Arrange the standard deviations in descending order to find the department with the highest standard deviation.

For example, let's say we have the salaries data for three departments:

DepartmentSalariesDepartment A$50,000, $55,000, $60,000Department B$45,000, $50,000, $55,000Department C$40,000, $45,000, $55,000

Calculating the mean, variance, and standard deviation for each department:

For Department A:

Mean: ($50,000 + $55,000 + $60,000) / 3 = $55,000

Squared differences: $(55,000 - $50,000)^2, $(55,000 - $55,000)^2, $(55,000 - $60,000)^2

Variance: [$(55,000 - $50,000)^2 + $(55,000 - $55,000)^2 + $(55,000 - $60,000)^2] / 3 ≈ $33,333.33

Standard deviation: √($33,333.33) ≈ $182.57

Similarly, you can calculate the mean, variance, and standard deviation for Department B and Department C. Finally, arrange the standard deviations in descending order to determine which department has the highest standard deviation.