11. (4 pts) The following statistics provide information about the scores on a national mathematics exam.
Mean 312 First Quartile 201
Median 296 Third Quartile 423
Mode 326 49th Percentile 307
a) What score did half of the test takers surpass?
b) What was the most common score?
c) What percentage of the test takers scored 201 or better?
d) If Joe had a score of 307, explain the meaning of his score
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a) To find the score that half of the test takers surpass, we can use the median. The median represents the middle score when the scores are arranged in ascending order. In this case, the median is 296. Since half of the test takers scored below the median and the other half scored above it, the score that half of the test takers surpassed is 296.
b) The most common score is given by the mode. The mode represents the score that appears most frequently in the dataset. In this case, the mode is 326, which means that it is the most common score among the test takers.
c) To determine the percentage of test takers who scored 201 or better, we can use the quartiles. The first quartile represents the score below which 25% of the test takers scored, and the third quartile represents the score below which 75% of the test takers scored. In this case, the first quartile is 201, which means 25% of the test takers scored 201 or below. To find the percentage of test takers who scored 201 or better, we subtract 25% from 100%. Therefore, the percentage of test takers who scored 201 or better is 100% - 25% = 75%.
d) If Joe had a score of 307, his score can be explained in relation to the percentile. In this case, the 49th percentile is given as 307. The 49th percentile represents the score below which 49% of the test takers scored. Therefore, we can say that Joe's score of 307 is higher than 49% of the test takers but lower than 51% of the test takers.