Statistics - Part 4. Percentile Rank

Statistics - Part 4 Percentile Rank

Percentile A percentile is a number from 1 to 99 that shows what percentage of the values in a data set are lower than a given value Percentiles are used to organize sets of data, such as test scores, so you can see how one score compares to others in a set

Percentile Rank Percentile rank tells you the percentage of values in a set of data that are lower than a given value Perhaps you got a score of 8/10 in a classroom quiz is that a good result? how would you know? Percentile ranks can help you assess how well you did on a quiz compared to other students

Consider the quiz scores marked on the line plot below. The quiz was out of 10 and the s represent each student who earned that score. 0 1 2 3 4 5 6 7 8 9 10 Test Scores

One student earned 10/10 on the quiz. What percentile ranking has this student obtained? Look at the number of students who scored below 10/10 nine students scored lower. Thus, 90% of the students scored less than the student who scored 10/10. The student who earned 10/10 is in the 90th percentile

Formula Percentile Rank = PR = b + 0.5E n *b is the number of values below the given score* *E is the number of scores equal to the given score, including the given score (if there are no other scores equal to the given score, then E = 1) *n is the total number of values in the data set*

Using the formula and the previous example: What is the percentile ranking for the students who earned 8/10? 0 1 2 3 4 5 6 7 8 9 10 Test Scores

Using the formula and the previous example: What is the percentile ranking for the students who earned 8/10? b + 0.5E PR = PR = n 7 + 0.5(2) 10

Using the formula and the previous example: What is the percentile ranking for the students who earned 8/10? b + 0.5E PR = PR = n 7 + 0.5(2) 10 PR = 80 th percentile

Zhinovia scores 82% on her biology exam. There were 199 other students who wrote the same exam. No one received the same score as she did, but 135 students received a lower score. What is her percentile ranking?

Remember! Notice that the percentile rank is not the percent score earned by the students. The percentile rank tells you the percentage of students who scored less, not the percent score earned on the quiz.

Jason wrote a math exam required for a job promotion. He earned a score of 73% on the test. If a total of 152 people wrote the exam, 4 people also scored 73%, and 62 scored lower than Jason, what is Jason s percentile ranking?

Jason wrote a math exam required for a job promotion. He earned a score of 73% on the test. If a total of 152 people wrote the exam, 3 people also scored 73%, and 62 scored lower than Jason, what is Jason s percentile ranking? b + 0.5E 62 + 0.5(4) PR = PR = n 200

Alexandre is the manager of a busy chain restaurant. At the end of each month the food sales of all the restaurant chain s locations in the province are compared to find out which location is the most successful. Out of 35 restaurants, Alexandre s restaurant is one of two restaurants in the 20th percentile. How many restaurants were more successful than Alexandre s?

To solve this we will use the formula for percentile rank to calculate how many restaurants earned less than Alexandre s (solve for b ). b + 0.5E b + 0.5(2) PR = 20 th = n 35 Please turn your attention to the white board for the solution b = 6

The answer (6 = b) tells us that there were 6 restaurants that earned less money than Alexandre s. Subtract your value for b from 35 to find how many restaurants were more successful than Alexandre s 35-6 = 29; There were 29 restaurants with higher sales than Alexandre s restaurant that month, therefore, 29 restaurants earned more money

Try These! As part of a graduation committee, Maria orders the graduation gowns for a class of 148 students. She knows that her percentile ranking for height is 75 and that 7 others are the same height as her. How many students are taller than Maria?