Math Problem Statement
In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force.
$ 356 $ 321 $ 361 $ 341 $ 347 $ 362
(a) Calculate x⎯⎯ , s2, and s for the expense data. (Round "Mean" and "Variances" to 2 decimal places and "Standard Deviation" to 3 decimal places.)
Solution
The calculations for the given expense data are as follows:
- Mean ():
- Variance ():
- Standard Deviation ():
Would you like further details or have any questions?
Here are five related questions for further exploration:
- How does the standard deviation help in understanding the variation in the expenses?
- What is the significance of using (sample variance) versus population variance?
- How would the results differ if the sample size was larger?
- Can you use this data to predict future expenses?
- What are some other cost-control strategies a company could use based on statistical analysis?
Tip: The standard deviation gives you an idea of how much the values in your data set differ from the mean, helping you assess variability.
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Sample Mean
Sample Variance
Standard Deviation
Formulas
Sample Mean (x̄) = (Σx) / n
Sample Variance (s²) = Σ(x - x̄)² / (n - 1)
Standard Deviation (s) = √s²
Theorems
Sample Mean Theorem
Sample Variance Theorem
Standard Deviation Formula
Suitable Grade Level
Grades 10-12
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