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Chapter 3: Problem 6

Compute the mean hourly wage paid to carpenters who earned the following wages: \(\$ 15.40, \$ 20.10, \$ 18.75, \$ 22.76, \$ 30.67, \$ 18.00 .\)

Short Answer

Expert verified
The mean hourly wage is approximately $20.95.

Step by step solution

01

Sum the Wages

To find the mean, start by adding up all the carpenters' wages. Calculate the sum: \[15.40 + 20.10 + 18.75 + 22.76 + 30.67 + 18.00\] The total is \(125.68\).
02

Count the Number of Observations

Count the number of different wage amounts given. There are six wages provided.
03

Calculate the Mean

Divide the total sum of the wages by the number of observations to find the mean wage: \[\frac{125.68}{6} \approx 20.95\] So, the mean hourly wage is approximately \(20.95\).

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Key Concepts

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

Hourly Wage
The concept of an hourly wage is quite straightforward. It refers to the amount of money a carpenter, or any professional, earns for each hour of work.
In this exercise, each carpenter has a specific hourly wage, such as $15.40 or $30.67.
Understanding hourly wages helps determine how much a worker earns during a typical work period, like an 8-hour day or 40-hour week.
Given multiple wages, it is important to calculate the average, or mean wage, to understand the typical earning across the group. This exercise is about determining that average wage, providing insight into the wage distribution.
Sum of Observations
In the context of calculating the mean hourly wage, the sum of observations is the total of all individual wages.
For this example, the observations are the wages earned by the carpenters.
The process involves adding these numbers together:
  • Start with the first wage: $15.40
  • Add $20.10 for the second wage, getting $35.50
  • Continue adding each subsequent wage:
    • $35.50 + $18.75 = $54.25
    • $54.25 + $22.76 = $77.01
    • $77.01 + $30.67 = $107.68
    • $107.68 + $18.00 = $125.68
The sum of all these wages is $125.68.
This total plays a critical role in calculating the average wage of the carpenters.
Number of Observations
For this exercise, the number of observations is simply the count of wage amounts provided.
Each wage represents an 'observation' in statistical terms.
In the given exercise, there are six wages:
  • $15.40
  • $20.10
  • $18.75
  • $22.76
  • $30.67
  • $18.00
This means that the number of observations is 6.
This count is crucial because the mean calculation requires dividing the sum of all observations by this number.
Mean Wage
The mean wage represents the average hourly wage paid to the carpenters.
To calculate the mean wage, you take the total sum of wages and divide it by the number of observations.
Here, the sum of the observations is \(125.68, and the number of observations is 6. The formula to find the mean wage is: \[\text{Mean Wage} = \frac{\text{Sum of Wages}}{\text{Number of Observations}} = \frac{125.68}{6}\] This calculation results in approximately \)20.95.
Interpreting the mean wage:
  • This means that, on average, each carpenter earns about $20.95 for every hour they work.
  • It gives a central value for wages, indicating what is common among the set of wages provided.
  • Understanding the mean wage helps both workers and employers assess how competitive or fair the wages are across a specific industry or region.

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Most popular questions from this chapter

The Split-A-Rail Fence Company sells three types of fence to homeowners in suburban Seattle, Washington. Grade A costs \(\$ 5.00\) per running foot to install, Grade \(B\) costs \(\$ 6.50\) per running foot, and Grade C, the premium quality, costs \(\$ 8.00\) per running foot. Yesterday, Split-A-Rail installed 270 feet of Grade \(\mathrm{A}, 300\) feet of Grade \(\mathrm{B},\) and 100 feet of Grade C. What was the mean cost per foot of fence installed?

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There are many financial websites that provide information on stocks by industry. For example, go to http://biz.yahoo.com and select Stock Research; under Analyst Research select Sector/Industry. There are many choices available here such as Energy, Financial, and Healthcare. Select one of these sectors, such as Healthcare. Another list of choices is now available; select one such as Major Drug. A list of companies in that industry will appear. Select one of the variables available, such as the price to earnings ratio, listed as \(\mathrm{P} / \mathrm{E}\). This variable is the ratio of the selling price of a share of the company's common stock to the earnings per share of common stock. Download this information into Excel and find the mean, median, and standard deviation. Go back to Sector/Industry and choose another Sector and Industry. You might want to select Energy and then Coal. A list of companies will appear. Select the same variable as before. Download the information to Excel and find the mean, median, and standard deviation for this industry. Compare the information on the two sectors. Write a brief report summarizing your findings. Are the means different? Is there more variability in one industry than another?
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