AMC 8 Data Analysis & Statistics 3

Question 1

The average of 6 numbers is 12. When one number is removed, the average of the remaining 5 is 11. What number was removed?

Accepted Answer

17

Answer

Total of 6 numbers = 72; total of remaining 5 = 55; the removed number = 72−55 = 17.

Question 2

Five quiz scores are 62, 75, 80, 85, and 88. If the lowest score is removed, by how much does the mean increase?

Accepted Answer

4

Answer

Original mean = 390/5 = 78; new mean = 328/4 = 82; the increase is 82−78 = 4.

Question 3

A histogram has intervals with frequencies: 0–10: 3, 10–20: 8, 20–30: 12, 30–40: 5. In which interval does the median fall?

Accepted Answer

20–30

Answer

Total = 28 values; the 14th and 15th values fall in the 20–30 interval (cumulative through 20 is 11).

Question 4

A data set of 8 values has a sum of 96. Three new values of 10, 12, and 14 are added. What is the new mean?

Accepted Answer

12

Answer

New sum = 96+10+12+14 = 132; new count = 11; mean = 132/11 = 12.

Question 5

In a box plot, Q1 = 20, median = 30, Q3 = 40, minimum = 10, maximum = 60. What is the interquartile range (IQR)?

Accepted Answer

20

Answer

IQR = Q3 − Q1 = 40 − 20 = 20.

AMC 8 - American Mathematics Competition 8 Practice Test