Calculating percentile

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 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 all right now let's work through this together so when you think about percentile you really want to think about so we 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 daily is six hours per day so let's see there are I'm just going to count them 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 fourteen hour oh six hours per day and so that would get us a number fifty percent with that that six hours is it the 50th percentile if we want to say what percentage is at that number 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 want to write that as the decimal let's see seven goes into four point zero zero zero easy to estimate so seven goes into forty five times 35 we subtract we get a five bring down a zero goes five times like it's just going to be 0.5 repeating so 55 point five five five five percent so either of these would actually be a legitimate response to the percentile rank for the driver with a 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 the roughly the 55th well 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 it's even that's reasonably close to either one of those and that's the 55th percentile 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