Which of the following statements correctly describes the mean salary of all female workers if it is $35000$?

• A. No female worker earns more than $35000$.
• B. The average salary of all female workers is $35000$.
• C. Half of the female workers earn less than $35000$.
• D. The most common salary among female workers is $35000$.

Answer: (B)

Verified step by step guidance

1. Understand that the mean (average) salary is calculated by summing all individual salaries and dividing by the number of female workers. It represents the central tendency but does not imply anything about individual salaries directly.
2. Recognize that the statement 'No female worker earns more than 35000' is not necessarily true just because the mean is 35000; some salaries could be above or below this value as long as the average balances out.
3. Note that the mean being 35000 does not guarantee that half of the female workers earn less than 35000. This describes the median, which is a different measure of central tendency.
4. Understand that the most common salary (mode) being 35000 is also not implied by the mean. The mode is the salary that appears most frequently, which can be different from the mean.
5. Conclude that the correct interpretation of the mean salary being 35000 is simply that the average salary of all female workers is 35000, without making assumptions about individual salaries or their distribution.