Question

scores on a mathematics assessment test for eighth - graders have a mean of 281, a 10th percentile of 231, a 25th percentile of 251, a 75th percentile of 301, and a 90th percentile of 329. interpret each of these numerical descriptive measures. interpret the mean value of 281. choose the correct answer below. a. for this problem, the mean value of 281 represents the range of test scores on a mathematics assessment test for eighth - graders. b. for this problem, the mean value of 281 represents the variation in the test scores on a mathematics assessment test for eighth - graders. c. for this problem, the mean value of 281 represents the middle test score when the scores are arranged in ascending (or descending) order. d. for this problem, the mean value of 281 represents the average test score on a mathematics assessment test for eighth - graders. a 10th percentile of 231 means that 10 % of the scores fall below 231 and 90 % of the scores fall above 231. a 25th percentile of 251 means that 25 % of the scores fall below 251 and 75 % of the scores fall above 251. a 75th percentile of 301 means that 75 % of the scores fall below 301 and 25 % of the scores fall above 301. a 90th percentile of 329 means that 90 % of the scores fall below 329 and 10 % of the scores fall above 329.

Explanation:

Step1: Recall percentile definition

The $p$ - th percentile of a data - set is a value such that $p$% of the data values are less than or equal to it.

Step2: Interpret each percentile

For the 10th percentile of 231: 10% of the scores fall below 231 and 90% of the scores fall above 231.
For the 25th percentile of 251: 25% of the scores fall below 251 and 75% of the scores fall above 251.
For the 75th percentile of 301: 75% of the scores fall below 301 and 25% of the scores fall above 301.
For the 90th percentile of 329: 90% of the scores fall below 329 and 10% of the scores fall above 329.
The mean value of 281 represents the average test score on a mathematics assessment test for eighth - graders.

Answer:

A 10th percentile of 231 means that 10% of the scores fall below 231 and 90% of the scores fall above 231.
A 25th percentile of 251 means that 25% of the scores fall below 251 and 75% of the scores fall above 251.
A 75th percentile of 301 means that 75% of the scores fall below 301 and 25% of the scores fall above 301.
A 90th percentile of 329 means that 90% of the scores fall below 329 and 10% of the scores fall above 329.
For this problem, the mean value of 281 represents the average test score on a mathematics assessment test for eighth - graders.