Mr. Ironheart came in to rescue the Troubleland Company. He immediately announce

Question

Mr. Ironheart came in to rescue the Troubleland Company. He immediately announced a massive layoff the day he took over as the Chairman. He said that the layoff is necessary because the payroll of this company has run out of control. In the last two years, he claimed, the average payroll had increased by 17%. The employee union's President denounced the layoff decision, and countered that the average employee's income increased merely 1% over the last two years, far below the inflation. "The best way to cut the payroll, " the President said, "is to fire (Mr. Ironheart) himself, who is paid over 80 million dollars a year to take over the CEO position." Which of these two is using the mean and which is using the median when discussing the payroll increase? And who do you think is right?

Explanation / Answer

When the new CEO took over the position, since he is paid a very high salary, the total payroll increased considerably. That increase will be reflected only in the mean, not in the median. Because even if only 1 new employee is added to the company who is having very high salary, this wont affect the median salary. But this salary will be counted when the mean salary is calculated. So, Mr. Ironheart is using mean while discussing the payroll and the president of the employees union is using the median for discussing the payroll. Median cannot be used as the measure of central tendancy. The median can remain the same even if there are several addtions to the employees. The total payroll can go up without affecting the median. So, it is preferable to use mean as the measure of central tendancy. Also, we exactly dont know if there is increase in employee strength, because we are not sure if its the salary of the CEO alone that is resulting in the 17% increase in payroll. Since Mr.Ironheart is using the better representative measure of central tendency, we can say that Mr.Ironheart is right.

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