Math Problem Statement

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 50  43  46  59  34  34  50  43  46  31  59  50  49
​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a 6​% raise. Find the sample mean and sample standard deviation for the revised data set. ​(c) To calculate the monthly​ salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. ​(d) What can you conclude from the results of​ (a), (b), and​ (c)?

Solution

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Mean
Standard Deviation
Percentage Increase
Scaling Data

Formulas

Sample Mean: x̄ = (Σxᵢ) / n
Sample Standard Deviation: s = √[Σ(xᵢ - x̄)² / (n - 1)]
Revised Salary with 6% Raise: New Salary = Old Salary × 1.06
Monthly Salary: Monthly Salary = Annual Salary / 12

Theorems

Properties of Mean and Standard Deviation under Scaling

Suitable Grade Level

Grades 10-12