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
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