okay so we are back to part two section 2.3 and we're gonna um continue with percentiles and we're gonna look at finding the K percentile so in other words we have our list of data and we want to know where's the 10th percentile which what number is that um so this is a formula to get that so let's look at some variables so we have k k is the kit percentile which may or may not be in our data set I is the index ranking or position of the data value so I represents where you're going to find that percentile that you're looking for n is the total number of data so how many numbers are in your data set so the first thing you need to do is order your data set from smallest to largest okay just like we've done before and here's the formula I is equal to K divided by a hundred times n so there are two situations when you do this formula you might have I if it's not a whole number so in other words if you get a decimal then you would round up to the next whole number and the value of the case percentile is the ith value starting from the lowest value okay so the position of your answer is the next whole number the other situation would be is if I is a whole number the percentile is between the ith value in the next data value find the mean of the two values so then in that case if you have a whole number you're going to find that price value and then the next value and take the average of the two so we're going to practice this so you can see what it looks like so example three we have listed are 28 ages of academic award-winning best actors in order from smallest to largest okay so they have the numbers in order so that's good and our for part A we want to find the 70th percentile so let's use our formula to do this so our formula is I is equal to K divided by 100 times n so I equals equals so I equals K in this case k is 70. divided by a hundred times n and we know that we have 28 pages so n is 28. [Music] okay so put that in your calculator and we get what do we get we get 19.6 okay So This falls in the first category I is not a whole number so because it's not a whole number I'm going to round up and that's going to equal 20. so 20 represents the position of your 70th percentile so I'm going to say 20th value okay so the 20th value is your answer so let's go to our list and find the 20th value one two three four five six seven eight 10 11 12 13 14 15 16 17 18 19 20. so this number 62 is your 20th value and that is your 70 70th percentile so I'm going to say that 62. okay now is the 70th percentile there we go I can say it the other way 70th percentile is 62. either way okay so that's my first answer the other thing I just want to mention that we always round up so let's say I had an answer of I I equals um let's say 5.2 okay so even though my two you see how the two the decimal two it's below five it doesn't matter it's still just not a whole number so when it says that we round up think about that that we always round up okay so here I'm going to say always round up so in this case I would have to look at the sixth value for my answer I'm going to put that in parentheses it's just a side note um that we always Round Up regardless if um the number the desperate whatever um regardless of the number of the decimal okay whether it's above five or below five it doesn't matter we always round up okay so let's move on to Part B so on this one we're looking for the 25th percentile so let's use our formula again I equals um our K in this case is 25 divided by a hundred times 28. [Music] blue so you can see this is what I've typed in okay so if you put that in your calculator this time we get a seven okay so this time it's a whole number so if it's a whole number it says the percentile is between the the ice value and the next data value so it's in between the seventh and the eighth value so to find that I need to find the mean or the average of those two numbers so let's go to our data set and find the seventh and eighth value one two three four five six seven here's my seventh and my eighth values okay so 29 and 30. so I need to find the average of those numbers so 29 Plus 30. divided by 2 equals 29.5 okay so it looks like my answer is 29.5 is the 25th there we go okay so that's how you find percentiles the location of the number of the percentile