Difference between revisions of "2022 AMC 8 Problems/Problem 19"
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== Solution == | == Solution == | ||
− | The median is the average of the <math>10^\text{th}</math> and <math>11^\text{th}</math> scores. | + | The median is the average of the <math>10^\text{th}</math> and <math>11^\text{th}</math> scores. In order to minimize the number of changed scores, the <math>10^\text{th}</math> score must be <math>85</math>. |
In progress please do not edit | In progress please do not edit |
Revision as of 18:48, 28 January 2022
Problem
Mr. Ramos gave a test to his class of students. The dot plot below shows the distribution of test scores.
Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students extra points, which increased the median test score to
. What is the minimum number of students who received extra points?
(Note that the median test score equals the average of the scores in the middle if the
test scores are arranged in increasing order.)
Solution
The median is the average of the and
scores. In order to minimize the number of changed scores, the
score must be
.
In progress please do not edit