Worked+Problems+-+Percentiles

Joseph Thorne Problem 1: //936 people were surveyed, and 338 had cars that got less than an estimated 25mpgs. Tatiana’s 2009 Mini Cooper Clubman gets an estimated 25mpgs. What is the percentile rank for Tatiana’s Mini?// To find a percentile rank, you divide the number of values below the value you are calculating, by the total number of values in the data set. You then multiply this by 100 becuase it will be a decimal and we need it to be a whole number. This is represented by this formula: //(p=percentile rank, b=number of values below the target value, n=the total number of values)// We know that 936 mpg ratings were recorded, so 936 is the total number of values in the data set. The problem also says 338 cars got less than 25mpgs. Since Tatiana’s Mini gets 25mpgs, we know she has a higher mpg rating than 338 people. We enter these values into the equation: We are left with an answer of 36.1111, but we’ll round this to 36. Tatiana’s Mini scores in the 36th percentile of the cars tested for mpgs. Example Problem 2: //Now let’s say Tatiana traded in her Mini a few years later for a Prius that averages 42mpgs. She particiaptes in the survey along with 418 others. 113 of the cars got an estimated 42mpgs or more. What is her percetile rank for mpgs?// First, I would need to find the number of cars with a lower mpg rating than Tatiana’s (b), then I would divide it by the total number of cars in the survey (n). Don’t get tricked! The problem says that 113 cars got the **same** or **higher** mpg rating than the Prius. We need to find the number of cars who had a **lower** mpg rating. So we subtract the number of those who have the same or greater mpgs from the total: There are 305 cars that have a lower mpg rating that Tatiana’s. We have enough information for the equation now: We’ll round our answer of 72.96 to 72. Tatiana’s Prius scores in the 72nd percentile.
 * “But what’s the difference between a percentile rank and a percentage score?”** Well, I’m glad you asked. Let’s say Tatiana’s Mini had scored 98% on the road safety test. But what does that mean? Tatiana doesn’t know what the test is about or how other cars scored. How can there be one number that tells her how her car’s safety compares to others? The percentile rank! It would have been more helpful if she knew that her Mini scored in the highest percetile, because this tells her it’s one of the safest cars on the market, as opposed to a test percentage score that means almost nothing to her.