AMC 8 Data Analysis & Statistics 2 — Questions and Answers
Question 1: A student scored 80, 85, 90, and 75 on four tests. What score is needed on the fifth test to achieve an average of 85?
- 90
- 92
- 95 (Correct answer)
- 88
Correct answer: 95
The sum of 5 scores must be 85×5=425; current sum is 330, so the fifth score must be 425−330=95.
Question 2: A stem-and-leaf plot shows: Stem 4: leaves 2,5,8; Stem 5: leaves 1,3,7; Stem 6: leaves 0,4. What is the median?
- 53
- 55 (Correct answer)
- 57
- 51
Correct answer: 55
The 8 values are 42,45,48,51,53,57,60,64; the median is the average of the 4th and 5th values: (53+57)/2=55.
Question 3: A class of 10 boys has an average score of 75, and a class of 15 girls has an average score of 80. What is the combined class average?
- 77
- 77.5
- 78 (Correct answer)
- 78.5
Correct answer: 78
Combined average = (10×75 + 15×80)/(10+15) = (750+1200)/25 = 1950/25 = 78.
Question 4: The data set {4, 7, 9, x, 12} has a mean of 8. What is the value of x?
- 6
- 7
- 8 (Correct answer)
- 9
Correct answer: 8
(4+7+9+x+12)/5 = 8 means 32+x = 40, so x = 8.
Question 5: Scores of 60, 70, 80, and 90 in a frequency table have frequencies of 2, 5, 8, and 5. What is the mode?
- 70
- 75
- 80 (Correct answer)
- 90
Correct answer: 80
The mode is 80 because it has the highest frequency of 8 occurrences.
Question 6: A store's daily sales: Mon=$200, Tue=$250, Wed=$180, Thu=$300, Fri=$270. On which day did sales increase the most from the previous day?
- Tuesday
- Wednesday
- Thursday (Correct answer)
- Friday
Correct answer: Thursday
Thursday's increase was $300−$180=$120, which is greater than Tuesday's $50 increase; Wednesday and Friday were decreases.
Question 7: In the data set {3, 5, 7, 9, 11}, the largest value changes from 11 to 21. Which measure of central tendency changes?
- Mean only (Correct answer)
- Median only
- Both mean and median
- Mode only
Correct answer: Mean only
The median is still the middle value 7, but the mean increases because the sum is larger; mode is unchanged.
AMC 8 Data Analysis & Statistics 2
A student scored 80, 85, 90, and 75 on four tests.
What score is needed on the fifth test to achieve an average of 85?