AMC 8 Data Analysis & Statistics 2

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?

Accepted Answer

95

Answer

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?

Accepted Answer

55

Answer

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?

Accepted Answer

78

Answer

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?

Accepted Answer

8

Answer

(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?

Accepted Answer

80

Answer

The mode is 80 because it has the highest frequency of 8 occurrences.

AMC 8 - American Mathematics Competition 8 Practice Test