Algebra II : Percentiles
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : Percentiles
Above is the stem-and-leaf display for a group of test scores. At what percentile would the student who made a score of 86 be?
None of the other responses is correct.
The stem-and-leaf display represents 53 scores. The "stems" (or left column) represent the tens digits, and the "leaves" in each row represent units digits, so the scores are
The student who scored an 86 outscored 42 of the students, or
of them. Since percentile is given to the nearest whole number, the correct response is 79.
Example Question #1 : Percentiles
Find the 85th percentile score in the following test results.
{95, 88, 70, 75, 83, 70, 66, 91, 68, 76, 82}
{95, 88, 70, 75, 83, 70, 66, 91, 68, 76, 82}
Arrange the values in numerical order.
{66, 68, 70, 70, 75, 76, 82, 83, 88, 91, 95}
Use the following to calculate percentile-
where 
This number gives of the location of the 85th percentile in our ordered set. Since it is not a whole number, round up, which will give us 10.
The 85th percentile score is the 10th value in our set, which is 91.
Example Question #3 : Percentiles
If a student is ranked eight out of ten in a competition, what is the student's percentile rank?
The formula to calculate a percentile rank is:
where 
Substitute the values into the formula.
Example Question #4 : Percentiles
The times for a six-mile race are shown below.
Sean: 
Ankur: 
Sarah: 
Fred: 
Ron: 
Jareth: 
Determine which percentile Sean's time is in.
First arrange the runners in order of fastest to slowest times:
Ron
Sarah
Jareth
Sean
Ankur
Fred
There are six runners so there will be six different percentiles, each seperated by 
Then each runner is in the following percentiles:
Ron - 
Sarah - 
Jareth - 
Sean - 
Ankur - 
Fred - 
As you can see, Sean is in the 
Example Question #1 : Percentiles
In a litter of nine kittens, the only orange kitten weighs more than three in the litter, and less than the other remaining five.
What is the percentile of the orange kitten's weight in comparison to the litter?
The percentile is equal to how many items in the set are equal to or less than the one in question divided by the total number of items in the set.
Because there are four items equal to or less than the orange kitten's weight and there are nine items total in the set, the percentile is equal to
Example Question #1 : Percentiles
98, 99, 99, 100, 101, 102, 104, 104, 105, 105, 107, 110, 112, 112
For the above data set, 102 is in what percentile?
50th
1st
57th
43rd
43rd
In the data set, 102 is the 6th data point listed. There are 14 data points total. This means that 
Example Question #1 : Percentiles
98, 99, 99, 100, 101, 102, 104, 104, 105, 105, 107, 110, 112, 112
For the above data set, 110 is in what percentile?
90th
86th
75th
14th
86th
The number 110 is the 12th in the list of 14 data points. That means that 
Example Question #8 : Percentiles
Above is the stem-and-leaf display for a group of test scores. Which of the following scores would come closest to being at the 
The stem-and-leaf display represents 53 scores. The score at the 35th percentile would be the score that is greater than 35% of the scores, or
Rounding, we count 19 scores from the bottom:
The score represented is 64, which is the correct response.
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