Math Problem Statement
a random sample of employee salaries at a company is shown below, 80, 56, 116, 62, 68, 127, 22, 119, 79, 132, 41, 72, 72, 81, 85 find the mean find the standard deviation find the variance
Solution
The calculations for the employee salaries are as follows:
- Mean (average) salary: 80.8
- Standard deviation: 31.40
- Variance: 986.03
Would you like a deeper explanation of these concepts or further details?
Here are 5 related questions you might find useful:
- How do you calculate the mean of grouped data?
- How does standard deviation help in understanding salary distributions?
- What is the difference between sample variance and population variance?
- How would the inclusion of an outlier affect the mean and standard deviation?
- Can we calculate the median salary from this data?
Tip: Standard deviation shows how much variation exists from the average, giving insights into how spread out the salaries are.
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion
Formulas
Mean: (Σx) / n
Standard Deviation (σ or s): sqrt(Σ(x - μ)² / n) for population or sqrt(Σ(x - x̄)² / (n - 1)) for sample
Variance (σ² or s²): Σ(x - μ)² / n for population or Σ(x - x̄)² / (n - 1) for sample
Theorems
Law of Large Numbers
Chebyshev's Inequality (related to variance)
Suitable Grade Level
High School (Grades 10-12) or College Introductory Statistics
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