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.)

The calculations for the given expense data are as follows:

- Mean ($\overline{x}$): $348.00$
- Variance ($s^2$): $241.60$
- Standard Deviation ($s$): $15.543$

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How does the standard deviation help in understanding the variation in the expenses?
2. What is the significance of using $s^2$ (sample variance) versus population variance?
3. How would the results differ if the sample size was larger?
4. Can you use this data to predict future expenses?
5. 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.

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 x̄, s², and s for the expense data. (Round 'Mean' and 'Variances' to 2 decimal places and 'Standard Deviation' to 3 decimal places.)

Learn how to calculate the sample mean, variance, and standard deviation for a random sample of entertainment expenses: $356, $321, $361, $341, $347, $362. This step-by-step guide is designed for students in Grades 10-12 and covers key statistical concepts used in business cost control.

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