Question

scores on a mathematics assessment test for eighth - graders have a mean of 284, a 10th percentile of 228, a 25th percentile of 257, a 75th percentile of 308, and a 90th percentile of 328. interpret each of these numerical descriptive measures.
interpret the mean value of 284. choose the correct answer below.
a. for this problem, the mean value of 284 represents the variation in the test scores on a mathematics assessment test for eighth - graders.
b. for this problem, the mean value of 284 represents the range of test scores on a mathematics assessment test for eighth - graders.
c. for this problem, the mean value of 284 represents the average test score on a mathematics assessment test for eighth - graders.
d. for this problem, the mean value of 284 represents the middle test score when the scores are arranged in ascending (or descending) order.
a 10th percentile of 228 means that 10% of the scores fall below 228 and 90% of the scores fall above 228.
a 25th percentile of 257 means that % of the scores fall below and % of the scores fall above.

Explanation:

Step1: Recall the definition of percentile

A \(p\)th percentile of a data set is a value such that \(p\%\) of the data values are less than or equal to it and \((100 - p)\%\) of the data values are greater than or equal to it.

Step2: Apply the definition to the 25th percentile

For the 25th percentile:

• The percentage of scores below the 25th percentile value is \(25\%\)
• The percentage of scores above the 25th percentile value is \(100 - 25=75\%\)
• The 25th percentile value is \(257\)

Answer:

A 25th percentile of 257 means that \(25\%\) of the scores fall below \(257\) and \(75\%\) of the scores fall above \(257\).