Students taking a make-up test receive the following grades: 95, 78, 94, 88, 65, 81, 91, 75, 89, and 76. Which grade has a percentile rank of 30? The test score with a percentile rank of 30 is
75.
To find the score with a percentile rank of 30, we need to first arrange the grades in order from lowest to highest: 65, 75, 76, 78, 81, 88, 89, 91, 94, 95.
Next, we calculate the percentile rank for each score using the formula:
percentile rank = (number of scores below the given score / total number of scores) x 100
For example, the percentile rank for a grade of 75 is:
percentile rank = (2 / 10) x 100 = 20
This means that 20% of the scores are below 75. To find the score with a percentile rank of 30, we need to keep adding up the percentages until we reach a score with a percentile rank of at least 30.
percentile rank for 65 = 0
percentile rank for 75 = 20
percentile rank for 76 = 30
Therefore, a grade of 76 has a percentile rank of 30 on this test.
To find the grade with a percentile rank of 30, we need to arrange the grades in ascending order:
65, 75, 76, 78, 81, 88, 89, 91, 94, 95
Next, we calculate the number of grades that fall below the 30th percentile. To find the percentile rank of a grade, we use the formula:
Percentile Rank = (Number of scores below the grade / Total number of scores) * 100
Using this formula, we can determine the percentile rank for each grade:
65 -> (0/10) * 100 = 0%
75 -> (1/10) * 100 = 10%
76 -> (2/10) * 100 = 20%
78 -> (3/10) * 100 = 30%
Therefore, the test score with a percentile rank of 30 is 78.