Difference between revisions of "2014 AMC 12A Problems/Problem 5"
(Created page with "Problem 5 On an algebra quiz, 10\% of the students scored 70 points, 35\% scored 80 points, 30\% scored 90 points, and the rest scored 100 points. What is the difference between...") |
|||
| Line 1: | Line 1: | ||
Problem 5 | Problem 5 | ||
| − | On an algebra quiz, 10 | + | On an algebra quiz, 10% of the students scored 70 points, 35% scored 80 points, 30% scored 90 points, and the rest scored 100 points. What is the difference between the mean and median score of the students' scores on this quiz? |
| − | + | (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 | |
Solution | Solution | ||
| Line 8: | Line 8: | ||
The mean can solved by the following. 10\% of 70 is 7, 35\% of 80 is 28, 30\% of 90 is 27, and (100\% - 10\% - 35\% - 30\%) = 25\%. 25\% of 100 is 25. 7 + 28 + 27 + 25 = 87. | The mean can solved by the following. 10\% of 70 is 7, 35\% of 80 is 28, 30\% of 90 is 27, and (100\% - 10\% - 35\% - 30\%) = 25\%. 25\% of 100 is 25. 7 + 28 + 27 + 25 = 87. | ||
The median can be solved by finding the number present at the 50% mark, which is 90. | The median can be solved by finding the number present at the 50% mark, which is 90. | ||
| − | 90-87 equals 3, which is | + | 90-87 equals 3, which is (C) 3. |
Revision as of 18:07, 7 February 2014
Problem 5
On an algebra quiz, 10% of the students scored 70 points, 35% scored 80 points, 30% scored 90 points, and the rest scored 100 points. What is the difference between the mean and median score of the students' scores on this quiz? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Solution
The mean can solved by the following. 10\% of 70 is 7, 35\% of 80 is 28, 30\% of 90 is 27, and (100\% - 10\% - 35\% - 30\%) = 25\%. 25\% of 100 is 25. 7 + 28 + 27 + 25 = 87. The median can be solved by finding the number present at the 50% mark, which is 90. 90-87 equals 3, which is (C) 3.
