1. Sunday, March 06, 2016 Data Interpretation Mean Median Mode Practice Quiz Answer Key

2. The given pie-chart shows the percentage of children interested in each field. Find the number of students who are interested in music and dance from a group of 120 students. 1 30% + 25% = 55% 55% of 120 = 0.55  120 = 66 Music + Dance

3. 2 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car? Let x = Total Monthly Expenses 25% of total monthly expenses is food cost 25% of x = 450.25x = 450 x = 1800.25.25x 450.25 =

4. 2 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car? Let x = Total Monthly Expenses x = 1800 20% of 1800 = 0.20  1800 = 360 Car Expense

5. 3 The chart shows the keyboarding speeds of five students before and after a keyboarding course. Which student showed the smallest percent increase in speed? Speed Increase Percent Increase 40–25 = 15 43–25 = 18 38–20 = 18 42–24 = 18 50–30 = 20 15  25 =.60 =60% 18  25 =.72 =72% 18  20 =.90 =90% 18  24 =.75 =75% 20  30 =.67 =67%

6. 4 Based on the chart, which best approximates the total number of video rentals by premium members at Store B during the years 2000–2002? Premium Members Store B / 2000 – 2002 Total Video Rentals Store B / 2000 – 2002 12(500)+15(1000) +20(1250) = 46,000

7. 5 In the class survey chart, what percent of the students watch 4 to 6 hours of each night? 2 3 9 7 Percent

8. 6 The number of students who watch less than 1 hour or more than 7 hours of television is approximately what percent of the number of students who watch television each night? 2 3 9 7 = 0.24 = 24% Percent ≈ 25% Students watch

9. 7 Tom and Karen ate lunch at the ballpark. Tom ordered a frankfurter, fries, and a soda. Karen ordered a hamburger and a soda. They divided the total bill evenly. What was the difference between what Karen paid and what she should have paid?

10. 7 Total Bill = $4.50 + $3.50 = $8.00 Tom Frankfurter$2.00 Fries$1.50 Soda$1.00 Total$4.50 Karen Hamburger$2.50 Soda$1.00 Total$3.50 Bill divided evenly = $8.00  2 = $4.00 What Karen paid – What Karen should have paid $4.00 – $3.50 = $0.50

11. 8 The graph shows students in the twelth-grade honor roll from 1992 to 1996. What was the percent increase in the number of students who made honor roll from 1993 to 1995? Increase amount 125 135 = 135 – 125 = 10 Percent Increase = 0.08 = 8%

12. 9 The graph shows the number of people in the family of each student enrolled at the local high school. About how many students live in a family of fewer than 4 people? Total Percentage = 11.7% + 13.3% = 25% Number of students = 25% of 1,500 = 0.25  1,500 = 375

13. 10 The table shows the total number of copies of Book B that were sold by the end of each of the first 5 weeks of its publication. How many copies of the book were sold during the 3 rd week of its publication? Total Copies Sold End of 1 st week 3200 End of 2 nd week 5500 End of 3 rd week 6800 End of 4 th week 7400 End of 5 th week 7700 Copies Sold Each Week (Total Copies Sold present week minus total copies sold previous week) 1 st week 3200 2 nd week 5500 – 3200 = 2300 3 rd week 6800 – 5500 = 1300

14. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount Alyse $14,500 Discount = 8% of $22,000 = 0.08  22,000 = $1760 = 5% of $14,500 = 0.05  14,500 = $725

15. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount = $1760 Alyse $14,500 Discount = $725 Discount Price = $22000 – $1760 = $20240 = $14500 – $725 = $13775

16. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount = $1760 Alyse $14,500 Discount = $725 Discount Price = $20240 Discount Price = $13775 Difference in Discounted Prices $20240 – $13775 = $6465

17. 12 Marie is a repeat customer and pays a discounted price of $27,630 for her new car. What was the original retail price of her car before the discount? Note: Since the discounted price is $27630, the original price is a bigger value. So, the discount rate is 10%.

18. 12 Marie is a repeat customer and pays a discounted price of $27,630 for her new car. What was the original retail price of her car before the discount? Note: Since the discounted price is $27630, the original price is a bigger value. So, the discount rate is 10%. Discounted Price = Retail Price – Discount 27630 = x –.10x Let x = Retail Price Let.10x = Discount 27630=.90x Divide both sides by.90 30700= x METHOD #1

19. 12 Marie is a repeat customer and pays a discounted price of $27,630 for her new car. What was the original retail price of her car before the discount? Retail Price – Discount = Discounted Price 24560 = –.10(24560) METHOD #2Test each answer. 27,630 Test A 24560 = – 2456 27,630 22104  27,630 24867 = –.10(24867) 27,630 Test B 24867 = – 2487 27,630 22380  27,630

20. 12 Retail Price – Discount = Discounted Price 27630 = –.10(27630) METHOD #2Test each answer. 27,630 Test C 27630 = – 2763 27,630 24867  27,630 30393 = –.10(30393) 27,630 Test D 30393 = – 3039 27,630 27354  27,630 30700 = –.10(30700) 27,630 Test E 30700 = – 3070 27,630 27630 =27,630

21. 13 What was the average (arithmetic mean) amount of money, rounded to the nearest dollar, raised by S.A.D.D. each year? S.A.D.D. $300 $500 $400 S.A.D.D. Average

22. 14 What was the average (arithmetic mean) amount of money, rounded to the nearest dollar, raised by all the clubs in 1996? 600400 1996 Average 400350 250200

23. The chart represents the grades Ms. Green’s class received on the final exam in math. To the nearest integer, what is the class average? Points 5  75 = 375 7  80 = 560 9  85 = 765 8  90 = 720 4  95 = 380 3  100 = 300 3100 36 ≈ 86 Class Average 15

24. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #1 Let x = Fifth test score (1)(333+x) = (85)(5) 333 + x = 425 x = 92 16

25. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 83.6≠ 85 NO 16

26. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 84.2≠ 85 NO ? 16

27. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 84.6≠ 85 NO ? ? 16

28. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 85 NO ? ? ? YES 16

29. In a class of 28 students, 19 students average 76 on a test and the rest average 88. To the nearest integer, what is the class average? Total sum of tests scores for all 28 students Sum of test scores for 19 students Sum of test scores for 9 students =+ = 1444 + 792 = 2236 Class Average ≈ 80 17

30. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? Average of 11 tests (1)(Sum of 11 tests) = (85)(11) Sum of 11 tests = 935 18

31. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? 85 + 1 = 86 Let x = Jame’s test score Sum of 11 tests = 935 Average with Jame’s test Sum of 11 tests + Jame’s test Number of tests = Average with Jame’s test 18

32. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? 85 + 1 = 86 Let x = Jame’s test score Sum of 11 tests = 935 Average with Jame’s test 1(935 + x) = (86)(12) 935 + x = 1032 –935 x = 97 18

33. 19 The average of 3 scores is twice the median. The median is 7 and the lowest score is 5. What is the highest score? Median = 7 Average of 3 scores = Twice median = 2(7) = 14 5, 7, ? Sum of 3 scores = 3(14) = 42 5 + 7 + ? = 42 12 + ? = 42 ? = 30

34. 20 If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a? a = 2bb = 3c a = 2(3c) a = 6c (1)(10c) = (40)(3) 10c = 120 c = 12

35. If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a? a = 2bb = 3c a = 2(36) Substitute c = 12 b = 3(12) b = 36 a = 2b a = 72 20

36. 21 The average of 7 test scores is 86. Four of the scores are 80, 83, 86, and 92. Which of the following could NOT be the other scores? Total Points = 7  Average = 7  86 = 602 Four scores total = 80 + 83 + 86 + 92 = 341 Total Points – Four scores total = Other scores total 602 – 341 = 261 Test A80 + 90 + 91 = 261YES Test B75 + 88 + 98 = 261YES Test C85 + 84 + 93 = 262NO

37. 22 The average of a and b is 5, and the average of c, d, and 10 is 24. What is the average of a, b, c, and d? Average of a and b is 5 Average of c, d, and 10 is 24 –10 Average of a, b, c, and d

38. 23 The ages of eight members of the student council include each age from 12 to 20, except 19. What is the median of these ages? 12, 13, 14, 15, 16, 17, 18, 20

39. 24 If x = 2 and y = 3, what is the value of the median of the following set? 2x + y, 2y – x, 2(x + y), 3x + y 2(2) + 3 4 + 3 7 2(3) – 2 6 – 2 4 2(2 + 3) 2(5) 10 3(2) + 3 6 + 3 9 4, 7, 9, 10 Write numbers in order: Median = 7 + 9 2 = 16 2 = 8

40. 25 Which of the following statements is necessarily true for the list of values: x, –x, y, –y, z, –z Average = x + (–x) + y + (–y) + z + (–z) 6 = 0 6 = 0 Answer: B