### Chap 16 Data Handling: 6 A.M. QUIZ (15 May 2010) (II)

Consider a company that has nine employees with salaries of \$35,000 a year, and their supervisor makes \$150,000 a year.

If you describe the typical salary in the company, which measure will you use - mean, median or mode? Explain your answer.

If you are the recruiting officer for the company and want to make a good impression on prospective employees, what would you tell them?

Source: Journal Writing in the Mathematics Classroom (Secondary)

Feedback to Responses (18 May 2010)
Most of the respondents have given very sound and good reasons on the choice to describe the typical salary, i.e. using MODE.
However, you may want to think deeper for the second part of the question. Is mean the best option?

1. I will use the mode if the typical salary is wanted. The difference between the supervisor's and the employees' salaries is too big. If I count the average by mean, it would be \$46500 per year. This would be dependent on the supervisor's salary, an only one supervisor can be appointed. Since, the employees' salary is the same, and they make up the majority of the company, the mode is the best way give the typical salary.

If you are the recruiting officer for the company and want to make a good impression on prospective employees, I would tell them the mean. When you are trying to attract someone to your company, the pay should be portrayed as a higher amount. Hence, telling them the mean, which is \$46500 per year, would be better than telling them the median and mode, which is \$35,000 a year.

2. I will use the mode if the typical salary is needed to be measured. The difference between the employee supervisor's and the employees' salaries is too much. If I use the mean to show the typical salary, it would be \$46500 per year. This typical salary is increased based on the supervisor's salary. In the company, there can be only one supervisor. Therefore, to have a better gauge of the salary, it will be better to use the mode as the employees' make up the majority of the company.

I would tell them the mean. When attracting an officer to your company, the pay should be shown higher as this would give a better impression on the prospective employees. Telling them the mean would be better than telling them the mode and median as the salary would seem lower. With a higher salary, they would be even more keen to join the company.

JJ(:

3. I will use the mode if the typical salary is to be calculated. The difference between the supervisor's salary and the employees' salaries is too huge. There is only one supervisor present in each company, and since the majority of the company is made up of employees, the mode would be my preferred way of calculating the typical salary.

I would tell them the mean salary, as a higher salary should be shown, in order to attract more people to the company. The mean salary is definitely higher than the mode and the median. (Although this is kind of cheating haha)

4. I will use mode if the topical salary is to be calculated. The difference between the supervisor's salary and the employees' salaries is like an outliner. As there is only one supervisor, the typical salary should be the employees' salary.

I will tell them the mean as the pay seems more attractive. Then people will come and then realize the truth. Haha!

5. I will use the mode of the salaries to calculate the typical salary of the company reason being that in the company there is only 1 supervisor where by the supervisor's salary and the employee;s salary has a difference of \$115,000 per year which is a very big difference. By using the mode, it would take the majority of the salaries, so the employee being the majority would be considered as the mode. Thats why using mode is the best to show the companies typical salary per year.

I would tell the recruits the mean pay as the mean pay would be higher over the mode and the median, because of that, our company would attract the recruits more easily.

6. I will definitely use the mode to calculate the typical salary.

First up, to recruit more employers, we need to inform them that the pay is good. In this case, it is \$35 000 per year. But then, we have to make sure the average is about the same as the employees' salary, otherwise the employees may feel that it is unfair that the average is so high, but their pay when compared to the average is mediocre.

So, in this case, we cannot use the mean, as the mean is the total sum of the wages (\$465 000 a year) divided by the number of total workers (10 workers including the supervisor himself) is equal to \$46 500. Meaning that if this is so, the employees would probably be expecting their pay to be above \$45 000, with the impression they can get from the average wages. Big difference, bad strikers. They would probably have gone on strike!

So, using the mode means the frequency of salary of most workers, which would probably be that of the workers themselves as the workers all have the same salary. Using the mode mean that, obviously, is similar to the "real" pay of the employees. So the employees would know the truth.

No more strikes!

7. I will use the mode if the typical salary is to be measured. There can be many employees but there can only be one supervisor. If we are calculating the typical salary in the company, we must use the method that provides the most accurate, which is the mode. There can be many employees but there can only be one supervisor. There is a significant difference in the employees and the supervisors salary, and the information would be misleading if the salary of the supervisor is included.

I will tell the recruit the mean pay of the company as the mean pay seems to be more attractive as it is higher as compared to the mode pay or the median pay. With a higher pay, more people are willing to work for the company. Hence, people will be attracted to work for the company.

8. The harder and smarter you work the more you will earn.

9. I will tell them that it is between \$35000 and \$150000 per year. It really depends on your position, and where you stand among the rest. If your rank is higher, you will get more pay.

10. I will tell the recruit the mode pay of the company.

11. I will tell them about the median but there will a increase of pay if they work harder.

12. I will tell them:

For the staff working in our company, most of them are getting \$35,000 a year. If you are outstanding on your performance and are promoted as the supervisor, we will give you \$150,000 a year.

13. I would tell them that the mode of each employees' salaries is \$35000.

14. If you are the recruiting officer for the company and want to make a good impression on prospective employees, what would you tell them?

I would tell them that the mode is actually \$35 000. I chose it as it is a measure of popularity and occurs most frequently.

15. If you are the recruiting officer for the company and want to make a good impression on prospective employees, what would you tell them?

I would tell them the mode. Telling them the mode that is close to a employees pay will help them to have a rough gauge of the exact pay. Honesty is a virtue.

16. I think mode as a measurement. The company has nine employees with salaries of \$35,000 a year and their supervisor makes \$150,000 a year. If I were to use mean, I will have \$(465000/10), which is \$46,500. It is too much and mediocre compared to the original income when measured by medium and mode, which is \$35,000. Using the frequency of the income may be better because it is much more reliable.

If you are the recruiting officer for the company and want to make a good impression on prospective employees, I will tell them the mode of income offered the company.

17. If you are the recruiting officer for the company and want to make a good impression on prospective employees, what would you tell them?

I would tell them the mode so when the prospective employees really become the company's employees, they will know that the company did not lie to them so they will not tell others that the company is not honest and less people will want to be the company's employee.

18. This comment has been removed by the author.

19. I will use the mode to calculate the typical salary in the company. There are many employees but only one supervisor, so we need to use the average that is most accurate, mode. There is a vast difference between the supervisor's and the employees' pay, thus to get the typical salary, we only count the employees' pay.

I will tell the prospective employees the mean, as using it will "increase" the amount each employee get due to the high salary of the supervisor, rather than giving the mode, which reduces the result, giving an impression that the pay is not high.

20. I would tell them the mode as it is not good to tell them the mean, then when they join the company they would see that their pay is lower than the mean, and that the company had given the mean as a gimmick to get them into the company.