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### Course: High school statistics > Unit 2

Lesson 3: Percentiles and z-scores# Calculating percentile

Learn how to calculate the percentile rank for a given data point.

## Want to join the conversation?

- shouldn't it be 57.14%02:57?(87 votes)
- You're correct. He made a mistake when dividing 7 into 50.(53 votes)

- I can see how we just guess and check to see whether we should use method 1 or 2, but supposed this is on the Free Response section of the exam? How should we know which definition of percentile to use?(25 votes)
- Percentiles for finite and/or discrete data sets tend to be ambiguous, because there are multiple reasonable definitions of percentile that could give different answers. If you are given a free response question about percentiles and you are not told which definition to use, it is best to explain which definition you are using.

Have a blessed, wonderful day!(23 votes)

- At2:50, shouldn't 7 go into 50 seven times, not five?(15 votes)
- Yes, Sal made a minor mistake. He thought that 4/7 equals 0.55 repeating. However 4/7 = 0.571428571. Hope this helped!(16 votes)

- Sal made a mistake when caculating 4/7, hesaid that it was about 0.55, but it is actually 0.571428...(13 votes)
- Yes, you're correct. Sal made a mistake in his calculation. The correct calculation of 4/7 is approximately 0.571428..., which is about 57.14%.(1 vote)

- Even though the answer is 57 % would you say the answer is 55 because that is the closest one?(11 votes)
- yes because 70 is much farther away than 55(5 votes)

- 7 goes into 50 7 times, not 5 times(9 votes)
- Wait a minute, did Sal make a mistake for the calculation of 7 divided by 4.000? Because I am pretty sure it should have been around 0.57...(6 votes)
- Hi!

How do I determine which "percentile method" to use (especially if the question is not multiple choice and I can't compare my answer with the ones given)?(5 votes)- The APA uses the "at or below" definition. I'd go with that.(1 vote)

- Why is the definition of percentile so loose?(4 votes)
- 1:44Pretty sure that I saw a third way to calculate a percentile rank: counting data points below plus
*half*of data points at the amount in question. Talk about ambiguity!(3 votes)

## Video transcript

- [Instructor] The dot plot shows the number of hours of daily driving time for 14 school bus drivers. Each dot represents a driver. So for example, one driver
drives one hour a day. Two drivers drive two hours a day. One driver drives three hours a day. It looks like there's five drivers that drive seven hours a day. Which of the following is the closest estimate to the percentile rank for the driver with a daily
driving time of six hours? And then they give us some choices. Which of the following
is the closest estimate to the percentile rank for the driver with the daily driving time of six hours? So pause the video and
see if you can figure out which of these percentiles
is the closest estimate to the percentile rank of a driver with a daily driving time of six hours, looking at this data right over here. Alright, now let's work
through this together. So when you think about percentile you really want to think about, so let me write this down. When we're talking about percentile we're really saying the percentage of the data that, and there's actually two ways
that you could compute it. One is the percentage of the data that is below the amount in question, amount in question. The other possibility is the percent of the data that is at or below, that is at or below the amount, the amount in question. So if we look at this right over here, let's just figure out
how many data points, what percentage of the data points are below six hours per day. So let's see, there are,
I'm just gonna count 'em. One, two, three, four, five, six, seven. So seven of the 14 are below six hours. So we could just say seven, if we use this first technique we would have seven of the 14 are below six hours per day, and so that would get us a number of 50%, that six hours is at the 50th percentile. If we want to say what percentage is at that number or below then we would also count this
one, so we would say eight, or eight out of 14. Eight out of 14, which is the same thing as four out of seven, and if we wanted to write that as a decimal, let's see, seven goes into four point zero zero zero, we just need to estimate. So seven goes into 40 five times. 35, we subtract, we get a five, bring down a zero, it goes five times. Look, it's just gonna be 0.5 repeating. So 55.5555%. So either of these would actually be a legitimate response
to the percentile rank for the driver with the daily
driving time of six hours. It depends on whether you
include the six hours or not. So you could say either
the 50th percentile or roughly the 55th, or actually the 56th percentile if you wanted to round to the nearest percentile. Now if you look at these choices here, lucky for us there's only one choice that's even, that's reasonably close to either one of those, and
that's the 55th percentile, and it looks like the people
who wrote this question went with the calculation of percentile where they include the
data point in question. So everything at six hours or less, what percentage of the total data is that?