You apply for a job selling diet marshmallows because an ad says that the average company employee earns $50,000 a year. Later you discover that the company has a president, a sales manager, and 30 salespeople; you also learn that each salesperson earns $14,000 a year. How can the company’s claim be correct?
A. The median is $50,000 because of high salaries for the president and sales manager.
B. The mean is $50,000 because of high salaries for the president and sales manager.
C. The median is higher than the mode.
D. The mode is $50,000 because of the high salaries for the president and sales manager.
To determine how the company's claim can be correct, we need to understand the concepts of mean, median, and mode in statistics.
- Mean: The mean is calculated by summing up all the values and dividing the total by the number of values. It represents the average value.
- Median: The median is the middle value when the data is arranged in ascending or descending order. If the number of values is even, the median is the average of the two middle values.
- Mode: The mode is the value that appears most frequently in the data set.
Given that there is a president, a sales manager, and 30 salespeople, and each salesperson earns $14,000 per year, we can deduce that the salaries of the president and sales manager must be higher than $14,000 for the average to be $50,000.
Now let's analyze each answer choice:
A. The median is $50,000 because of high salaries for the president and sales manager.
- This answer choice does not accurately address the given information. The median does not reflect the salaries of the president and sales manager.
B. The mean is $50,000 because of high salaries for the president and sales manager.
- This answer choice seems plausible. The mean would indeed be influenced by higher salaries for the president and sales manager.
C. The median is higher than the mode.
- This answer choice does not take into account the information about salaries. It is not possible to determine the relationship between the median and mode based on the given information.
D. The mode is $50,000 because of the high salaries for the president and sales manager.
- This answer choice incorrectly refers to the mode. The mode is the most frequently occurring value, which is unlikely to be $50,000 based on the given information.
Based on our analysis, the correct answer is B. The mean is $50,000 because of high salaries for the president and sales manager. The salaries of the president and sales manager would significantly affect the mean salary, bringing it closer to $50,000.