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Chapter 2: Problem 65

What is the mean weekly pay if 5 employees earn \(\$ 425\) per week, 3 earn \(\$ 750\) per week, and 1 earns \(\$ 1340 ?\)

Short Answer

Expert verified
The mean weekly pay is \$635.

Step by step solution

01

Determine the total earnings

Calculate the total weekly earnings for each group of employees. Multiply the weekly earnings by the number of employees for each group: \(5 \times \$425 = \$2125\), \(3 \times \$750 = \$2250\), and \(1 \times \$1340 = \$1340\).
02

Sum up the total earnings

Add up the total earnings from each group of employees to get the total pay for all employees: \(\$2125 + \$2250 + \$1340 = \$5715\).
03

Count the total number of employees

Add up the number of employees in each group: \(5 + 3 + 1 = 9\).
04

Calculate the mean

Divide the total pay by the number of employees to get the mean weekly pay: \(\$5715 \div 9 = \$635\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Total Earnings
In order to determine total earnings for a group of people, each subset of the group must be considered separately. For example, when calculating weekly pay, you will consider different pay rates for different employees.
In the given exercise, employees were divided based on how much they earned per week.
  • 5 employees earned \( \\(425 \) every week.
  • 3 employees earned \( \\)750 \) on a weekly basis.
  • 1 employee brought home \( \$1340 \) weekly.
To find the total earnings, multiply the wage by the number of employees in each category. Then, summing these results gives the total earnings of all employees combined.
This approach allows the consideration of varied pay levels in a group, leading to an accurate calculation of group earnings.
Sum of Values
After finding the total earnings for each group of employees, summing these individual totals gives the overall total earnings.
  • The sum process is simply adding together all the values found in the previous step.
  • In our example, the calculations were as follows: \( \\(2125 \) from the first group, \( \\)2250 \) from the second, and \( \\(1340 \) from the third.

Adding up \( \\)2125 + \\(2250 + \\)1340 \), you will get the total earnings, which is \( \$5715 \).
Summing values is a crucial step in various calculations as it aggregates individual data points into a single meaningful value.
This method assures us that we have accounted for all variations in income among employees.
Division
Division is a key process when you are looking to find the mean (or average) of a set of numbers. After summing up the total earnings, division is used to spread this total equally across all individuals.
In our scenario, the total earnings of \( \\(5715 \) need to be divided by the number of employees, which is 9.
This division gives the mean weekly pay : \[\text{Mean Weekly Pay} = \frac{\\)5715}{9} = \$635\]
Through division, we transform total earnings into a per-employee average pay.
This provides a clearer picture of standard earnings among employees within a varied pay structure.
Number of Employees
Counting the number of employees plays a vital role in calculating the mean pay for a group.
If one fails to include all employees in their count, the average earnings could be misrepresentative.
In the exercise, the employees are grouped based on their earnings:
  • 5 employees earning \( \\(425 \)
  • 3 employees making \( \\)750 \)
  • 1 earning \( \$1340 \)

Thus, when you add these up: \( 5 + 3 + 1 = 9 \)
The result of this addition gives the total number of employees: 9.
This number is essential as it serves as the divisor in the division step, ensuring the mean pay represents all employees fairly.

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