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Chapter 8 Test A

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Instructions: For each assigned problem show your complete solution in the left column under each problem. Show all work for each problem (using either MathType or Equation Editor) in order to receive credit. Be sure to reduce all fractions to lowest terms. If there is no work to show then explain in words how you solved the problem. Points will be deducted if there is insufficient explanation or work.

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Problems
(Enter your work and answer in this column) / Instructor’s comments
1. The pie chart shows the distribution of a person's total yearly income of $36,000. Find the amount budgeted for utilities.

Answer:
Utilities = 8% of $36,000 = 0.08 x 36000 = $2,880
2. Find the median of the following set of numbers.
11, 4, 9, 5, 6
Answer:
Arrangeset in ascending order:
4, 5, 6, 9, 11
Median is the middle number, which is6
3. The following scores were recorded on a 100-point examination:
95, 75, 76, 86, 96, 71, 68, 81, 95, 76, 69, 82, 93, 88, 94
Find the mean.
Answer:
Mean is the arithmetic average of all numbers
(95+75+76+86+96+71+68+81+95+76+69+82+93+88+94)/15
= 1245/15 = 83
4. Find the median of the following set of numbers.
33, 72, 23, 27, 77, 68, 85
Answer:
Arrange set in ascending order:
23, 27, 33, 68, 72, 77, 85
Median is the middle number, which is68
5. Use the bar graph, showing the attendance at a circus for 7 days in September, to find the median attendance over the 7 days.

Answer:
The numbers are:
4000, 5600, 3200, 4800, 6400, 7200, 5600
Arrange set in ascending order:
3200, 4000, 4800, 5600, 5600, 6400, 7200
Median attendance is the middle number, which is5,600
6. Find the mean of the following set of numbers.
13, 15, 18, 18, 18, 19, 22, 26, 28, 33
Answer:
Mean is the arithmetic average of all numbers
(13+15+18+18+18+19+22+26+28+33)/10
= 210/10 = 21
7. Find the mode of the following set of numbers.
15, 14, 10, 15, 16
Answer:
Mode is the number that appears most, which is 15
8. Use the graph, showing the yearly food costs of a family. What was the food cost in 2001?

Answer:
10 thousand dollars, i.e. $10,000
9. Use the graph below, showing the total U.S. motor vehicle production for the years 1996 to 2002, to answer the question.

What was the production in 2001?
Answer:
11.5 million cars
10. Liza kept the following records of her utility bills for 12 months:
$30, $25, $33, $29, $46, $31, $30, $63, $41, $40, $34, $30
(a) Find the mean of Liza's monthly utility bill.
(b) Find the median of Liza's monthly utility bill.
(c) Is the mean or median a more useful representative of Liza's monthly utility bills?
Answer:
Arrange set in ascending order:
25, 29, 30, 30, 30, 31, 33, 34, 40, 41, 46, 63
(a) mean is the arithmetic average = sum divided by number ofelements = 432/12 =36
(b) median is the middle number; since there are two numbers in the middle we take their average:
(31+33)/2 = 32
(c) mean is usually more useful
11. Find the mode of the following set of numbers.
16, 28, 30, 12, 16, 19, 22, 16
Answer:
Mode is the number that appears most, which is 16
12. Find the five-number summary of the following set of numbers.
349, 243, 119, 363, 246, 505, 263, 221, 324
Answer:
1- First arrange the set in ascending order:
119, 221, 243, 246, 263, 324, 349, 363, 505
2- Using the Rank method:
Lower quartile: 25% of the elements in the set are
below the lower quartile:
0.25*9=2.25, or 3rd element in the set, i.e., 243
Upper quartile: 25% of the elements in the set are
above the upper quartile:
0.75*9=6.75, or 7th element, i.e., 349
3- This, the five-number summary is:
minimum, lower quartile, median, upper quartile, maximum
119, 243, 263, 349, 505
13. Simplify:
–2.3 – (–8.8)
Answer:
-2.3 + 8.8 = 6.5
14. Multiply:
(1.3)(10)(–4)
Answer:
(1.3*10)(-4) = (13)(-4) = -52
15. Find the reciprocal of

Answer:

Reciprocal =
16. Which of the following numbers are integers?

Answer:
570, -670
17. Place the following set of numbers in ascending order.
25, –13, 8, –2, 13, 3, 18
Answer:
-13, -2, 3, 8, 13, 18, 25
18. Place the following set of numbers in ascending order.

Answer:

19. Simplify:

Answer:
-8.7 + 12.4 = 3.7
20. Place the following set of numbers in ascending order.

Answer:

21. Add:

Answer:

22. Simplify:

Answer:
2
23. Divide:

Answer:
-20
24. Evaluate:
|–15 + 8|
Answer:
|-7| = 7
25. Evaluate:
–82 – (–5)2
Answer:
-64-(25) = -89

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