[Math Center]

1. Each employee of a certain company is in either Department \(\)X\(\) or Department \(\)Y\(\), and there are more than twice as many employees in Department \(\)X\(\) as in Department \(\)Y\(\). The average (arithmetic mean) salary is $\(\)25,000\(\) for the employees in Department \(\)X\(\) and $\(\)35,000\(\) for the employees in Department \(\)Y\(\). Which of the following amounts could be the average salary for all of the employees of the company?
Indicate all such amounts.

(A) $\(\)26,000\(\)
(B) $\(\)28,000\(\)
(C) $\(\)29,000\(\)
(D) $\(\)30,000\(\)
(E) $\(\)31,000\(\)
(F) $\(\)32,000\(\)
(G) $\(\)34,000\(\)

 

2. Untitled1

For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car?

 

3.  Ellen has received the following scores on \(\)3\(\) exams: \(\)82, 74\(\), and \(\)90\(\). What score will Ellen need to receive on the next exam so that the average (arithmetic mean) score for the \(\)4\(\) exams will be \(\)85\(\)?

 

4.  The daily temperatures, in degrees Fahrenheit, for \(\)10\(\) days in May were \(\)61, 62, 65, 65, 65, 68, 74, 74, 75\(\), and \(\)77\(\).

(a) Find the mean, median, mode, and range of the temperatures.
(b) If each day had been \(\)7\(\) degrees warmer, what would have been the mean, median, mode, and range of those 10 temperatures?

 

 

5. The numbers of passengers on \(\)9\(\) airline flights were \(\)22, 33, 21, 28, 22, 31, 44, 50\(\), and \(\)19\(\). The standard deviation of these \(\)9\(\) numbers is approximately equal to \(\)10.2\(\).

(a) Find the mean, median, mode, range, and interquartile range of the \(\)9\(\) numbers.
(b) If each flight had had \(\)3\(\) times as many passengers, what would have been the mean, median, mode, range, interquartile range, and standard deviation of the \(\)9\(\) numbers?
(c) If each flight had had \(\)2\(\) fewer passengers, what would have been the interquartile range and standard deviation of the \(\)9\(\) numbers?

 

 

6. A group of \(\)20\(\) values has a mean of \(\)85\(\) and a median of \(\)80\(\). A different group of \(\)30\(\) values has a mean of \(\)75\(\) and a median of \(\)72\(\).

(a) What is the mean of the \(\)50\(\) values?
(b) What is the median of the \(\)50\(\) values?

 

 

7.

Quantity A Quantity B
The average of three numbers if the greatest is \(\)20\(\) The average of three numbers if the greatest is \(\)2\(\)

 

8. On the final exam in History \(\)101\(\), the average score for the girls was \(\)72\(\) and for the boys, \(\)70\(\).

Quantity A Quantity B
The average score for the class \(\)71\(\)

 

 

9.   Mr. Smith’s average annual income in each of the years \(\)1966\(\) and \(\)1967\(\) is x dollars. His average annual income in each of the years \(\)1968, 1969\(\), and \(\)1970\(\) is \(\)y\(\) dollars. What is his average annual income in the five continuous years \(\)1966\(\) through \(\)1970\(\)?

(A) \(\)2x/5 + 3y/5\(\)
(B) \(\)x/2 + y/2\(\)
(C) \(\)5(x + y)\(\)
(D) \(\)5x/2 + 5y/2\(\)
(E) \(\)3x/5 + 2y/5\(\)

 

10. The average temperature in New Orland from January through August is \(\)36\(\)°C. The minimum and the maximum temperatures between September and December are \(\)26\(\)°C and \(\)36\(\)°C, respectively.

Quantity A Quantity B
The average temperature for the year \(\)36\(\)°C

 

11.  The average of \(\)x, y\(\), and \(\)z\(\) is \(\)8\(\) and the average of \(\)y\(\) and \(\)z\(\) is \(\)4\(\).  What is the value of \(\)x\(\)?

(A) \(\)4\(\)
(B) \(\)9\(\)
(C) \(\)16\(\)
(D) \(\)20\(\)
(E) \(\)24\(\)

 

12.  The average of \(\)x\(\) and \(\)y\(\) is \(\)55\(\). The average of \(\)y\(\) and \(\)z\(\) is \(\)75\(\)

Quantity A Quantity B
\(\)z-x\(\) \(\)40\(\)

 

 

13. In Clarice’s class, each test weights her overall grade average three times as much as each quiz does. If Clarice scored \(\)88\(\) and \(\)94\(\) on two quizzes, respectively, and she scored \(\)90\(\) on the only test, what is her current overall grade average?
14.   What is the average of \(\)x, x-6\(\), and \(\)x + 12\(\)?

(A) \(\)x\(\)
(B) \(\)x + 2\(\)
(C) \(\)x + 9\(\)
(D) \(\)3x + 6\(\)
(E) It cannot be determined from the information given

 

15. The average of four numbers is \(\)12\(\). If the set of numbers includes \(\)9, 11\(\), and \(\)12\(\), what is the fourth number?

(A) \(\)12\(\)
(B) \(\)14\(\)
(C) \(\)16\(\)
(D) \(\)20\(\)
(E) \(\)24\(\)

 

 

Answer:

1  A ($\(\)26,000\(\)) and B ($\(\)28,000\(\)).
2  \(\)6,000\(\)
3  \(\)94\(\)
4 In degrees Fahrenheit, the statistics are
(a) mean=\(\)68.6\(\), median=\(\)66.5\(\), mode=\(\)65\(\), range=\(\)16\(\)
(b) mean=\(\)75.6\(\), median=\(\)73.5\(\), mode=\(\)72\(\), range=\(\)16\(\)
5
(a) mean=\(\)30\(\),median=\(\)28\(\),mode=\(\)22\(\), range=\(\)31\(\), interquartile range=\(\)17\(\)
(b) mean=\(\)90\(\), median=\(\)84\(\), mode=\(\)66\(\), range=\(\)93\(\), interquartile range=\(\)51\(\)
standard deviation=\(\)3\sqrt( \frac{ 940 }{ 9 } )\approx30.7\(\)
(c) interquartile range=\(\)17\(\),standard deviation\(\)\approx10.2\(\)
6 (a) mean=\(\)79\(\) (b) The median cannot be determined from the information given.
7 D
8 D
9 A
10 B
11 C
12 C
13 90.4
14 B
15 C

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