Chapter 12.4, Problem 17P

Ten students earned the following scores on a test: 89,90, 76, 78, 83,88, 91, 93, 96, and 90. Which score has a percentile rank of 90? Which score has a percentile rank of 10?

To determine

Find the score that has a percentile rank of 90 and that has percentile rank of 10.

Answer to Problem 17P

Score that has percentile rank of 90 = 93

Score that has percentile rank of 10 = 76

Explanation of Solution

Given:

Scores on a test:

89 , 90 , 76 , 78 , 83 , 88 , 91 , 93 , 96 , 90

Calculation:

Arrange the given scores in ascending order :

76 , 78 , 83 , 88 , 89 , 90 , 90 , 91 , 93 , 96

The percentile rank of a data value is the percentage of the data values less than or equal to the data value.

Percentile rank of the score is 90 means the percentage of number of scores less than or equal to the score is 90%= $\frac{9}{10}$ . Hence the number of scores less than or equal to the score are 9 , when there are 10 total number of scores given.

So, the score that has percentile rank of 90 is at 9^th position when all data values are arranged in ascending order = 93 .

Percentile rank of the score is 10 means the percentage of number of scores less than or equal to the score is 10%= $\frac{1}{10}$ . Hence the number of scores less than or equal to the score are 1 , when there are 10 total number of scores given.

So, the score that has percentile rank of 10 is at 1^st position when all data values are arranged in ascending order = 76 .