A small accounting firm has 4 accountants who each earn a different salary between 52,000 dollars and 58,000 dollars. For extra help during tax season, they hire a 5^("th ") accountant who earns 10,000 dollars. [Show data] How will hiring the 5^("th ") accountant affect the mean and median? Choose 1 answer: A Both the mean and median will decrease, but the median will decrease by more than the mean. (B) Both the mean and median will decrease, but the mean will decrease by more than the median. (c) The mean will decrease, and the median will increase. (D) The mean will increase, and the median will decrease.

Question

A small accounting firm has 4 accountants who each earn a different salary between 52,000 dollars and 58,000 dollars. For extra help during tax season, they hire a  5^("th ") accountant who earns 10,000 dollars. [Show data] How will hiring the  5^("th ") accountant affect the mean and median? Choose 1 answer: A Both the mean and median will decrease, but the median will decrease by more than the mean. (B) Both the mean and median will decrease, but the mean will decrease by more than the median. (c) The mean will decrease, and the median will increase. (D) The mean will increase, and the median will decrease.

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Determine Initial Mean Salary: Determine the initial mean salary of the 4 accountants. Since we do not have the exact salaries of the 4 accountants, we can only assume that they earn different salaries between $52,000 and $58,000. To find the mean, we would typically add all the salaries together and divide by the number of accountants. However, without specific values, we cannot calculate the exact initial mean.Determine Initial Median Salary: Determine the initial median salary of the 4 accountants. With 4 accountants, the median would be the average of the two middle salaries. Since the salaries are within a range and are different, the median would be between $52,000 and $58,000. Without specific values, we cannot determine the exact initial median.Calculate New Mean Salary: Calculate the new mean salary after hiring the 5th accountant. Let's assume the sum of the salaries of the 4 accountants is S. The new sum with the 5th accountant's salary would be S + $10,000. The new mean would be (S + $10,000) / 5. Since $10,000 is less than any of the initial salaries, adding this amount and dividing by 5 will decrease the mean salary.Determine New Median Salary: Determine the new median salary after hiring the 5th accountant. With 5 accountants, the median salary is the salary of the middle accountant when they are arranged in order. Since the 5th accountant earns $10,000, which is less than the lowest initial salary of $52,000, the median will remain the salary of the third accountant, which is between $52,000 and $58,000. Therefore, the median will not change.Choose Correct Answer: Choose the correct answer based on the calculations. From Steps 3 and 4, we know that the mean will decrease and the median will remain unchanged. This means that option (B) ＂Both the mean and median will decrease, but the mean will decrease by more than the median.＂ is incorrect because the median does not decrease. Option (C) ＂The mean will decrease, and the median will increase.＂ is incorrect because the median does not increase. Option (D) ＂The mean will increase, and the median will decrease.＂ is incorrect because the mean decreases and the median does not change. Therefore, the correct answer is option (A) ＂Both the mean and median will decrease, but the median will decrease by more than the mean.＂ even though the median actually remains the same, not decreases.

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