Understanding the Five Star Corporation's Workforce

The question asks for the total number of people employed by the 'Five Star' Corporation based on the provided table and notes. We are given information about the distribution of women staff in Professional and Managerial grades, along with some key notes about the overall workforce structure.

Analyzing the Given Information

We have the following data and notes:

• A table showing the number of women in different sub-categories of Professional and Managerial Grades.
• Note (a): There are five times as many men in Professional Grades as women.
• Note (b): The Corporation employs a total of 1300 staff in both Professional and Managerial Grades.
• Note (c): 8% of the total workforce at the Corporation is employed in Professional and Managerial Grades.

The question specifically asks for the total number of people the Corporation employs. To find this, we should look for a piece of information that relates the specific group (Professional and Managerial Grades) to the entire workforce.

Using the Key Notes to Find the Total Workforce

Let's focus on Note (b) and Note (c).

• Note (b) tells us that the total number of staff in both Professional and Managerial Grades combined is 1300.
• Note (c) tells us that this group (Professional and Managerial Grades) represents 8% of the total workforce of the Corporation.

This gives us a direct relationship between a specific number of employees (1300) and a percentage of the total workforce (8%). We can use this information to calculate the total number of employees in the entire Corporation.

Calculation Steps

Let 'T' represent the total workforce of the Corporation.

According to Note (c), 8% of the total workforce is equal to the number of staff in Professional and Managerial Grades.

According to Note (b), the number of staff in Professional and Managerial Grades is 1300.

Therefore, we can set up the equation:

$\text{8% of } T = 1300$

Converting the percentage to a decimal:

$\frac{8}{100} \times T = 1300$

Now, we solve for T:

$T = \frac{1300 \times 100}{8}$

$T = \frac{130000}{8}$

Let's perform the division:

$T = 16250$

So, the total number of people employed by the Corporation is 16250.

Verification of Data Consistency (Optional but helpful)

While not required to answer this specific question, we can quickly check if the table and Note (a) are consistent with Note (b).

• Total women in Professional Grades: $30 + 15 + 15 + 20 + 10 = 90$
• Note (a): Men in Professional Grades = 5 * Women in Professional Grades = $5 \times 90 = 450$
• Total staff in Professional Grades = Women + Men = $90 + 450 = 540$
• Total women in Managerial Grades: $25 + 1 + 4 = 30$
• Total staff in Professional and Managerial Grades = 1300 (from Note b).
• Total staff in Managerial Grades = Total Staff (Pro & Man) - Total Staff (Pro) = $1300 - 540 = 760$
• Men in Managerial Grades = Total Staff (Man) - Women (Man) = $760 - 30 = 730$

This calculation shows the distribution is internally consistent with Note (a) and (b), although calculating the total workforce only required Note (b) and (c).

Conclusion

Based on the information that 1300 staff are in Professional and Managerial Grades, and this represents 8% of the total workforce, we calculated the total number of people employed by the Corporation.

The total workforce is 16250.

Revision Table - Workforce Calculation

Additional Information - Percentage Concepts

This problem uses the concept of percentages to relate a part to a whole. Understanding how to work with percentages is crucial for data interpretation questions.

• Percentage Definition: A percentage is a number or ratio expressed as a fraction of 100. The symbol '%' is used to indicate a percentage.
• Converting Percentage to Decimal: To convert a percentage to a decimal, divide the percentage by 100. For example, 8% is $\frac{8}{100} = 0.08$.
• Finding the Whole when the Part and Percentage are Known: If you know that a certain value (the part) represents a specific percentage of a total value (the whole), you can find the total value using the formula:

  $\text{Whole} = \frac{\text{Part}}{\text{Percentage (as decimal)}}$

  In this problem:

  Part = 1300 (staff in Professional and Managerial Grades)

  Percentage = 8% or 0.08

  Total Workforce (Whole) = $\frac{1300}{0.08} = 16250$

• Importance in Data Analysis: Percentages are widely used in tables and charts to show proportions and distributions, making it easier to compare different parts of a dataset relative to the total.