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.
No statistics were provided
To answer these questions, we need to understand the statistics provided about the scores on the national mathematics exam.
a) To find the score that half of the test takers surpassed, we need to find the median. The median is given as 296, which means that half of the test takers scored below 296.
b) The most common score is referred to as the mode, and it is given as 326. Therefore, 326 is the most common score among the test takers.
c) To calculate the percentage of test takers who scored 201 or better, we can use the information provided about the first quartile and the third quartile. The first quartile is given as 201, which means that 25% of the test takers scored 201 or below. The third quartile is given as 423, which means 75% of the test takers scored 423 or below. To find the percentage of test takers who scored 201 or better, we subtract the first quartile value from 100% and add the percentage of test takers who scored 423 or below.
Percentage = 100% - 25% + 75% = 100% + 75% - 25% = 150%
So, 150% of the test takers scored 201 or better. Note that it is not possible to have a percentage greater than 100%, so it is likely that some of the values provided might be incorrect.
d) If Joe had a score of 307, his score is equal to the 49th percentile. This means that Joe scored better than 49% of the other test takers. In other words, he performed better than 49% of the students who took the exam.