[Music] welcome to math with mr j [Music] in this video i'm going to cover how to find the inter-quartile range of a data set now the inter-quartile range gives us the spread of the middle 50 of our data compared to just range which gives us the spread of the entire data set so let's jump into the two examples that we're going to go through together here in order to get this down now the first example we're going to do a data set with an odd number of numbers and the second example will be a data set with an even number of numbers let's jump into our first example here and the first thing we want to always do is put our data in ascending order which means least to greatest in the case of this example we are already in order so we can move to the next step which says find the median now steps two and three are kind of combined here these steps involve finding the quartiles the lower quartile the median and the upper quartile but the first thing we need to do is find the median as far as finding quartiles so the median is the middle of our data set in the case of this example we have seven numbers so we will have three numbers on the left three numbers on the right and the number in the middle will be our median it's going to be 38. so down here where it says q2 50th percentile i'm going to write 38 q2 stands for quartile 2 which is the same as the median so q2 50th percentile and median all mean the same thing so once we have the median we can find the lower and upper quartiles let's start with the lower so we'll take a look at the lower half here and we need to find the middle of that lower half the median of the lower half it's going to be this 32 here since we have three numbers it's going to be the middle one so q1 quartile 1 means lower quartile so let's write 32. upper quartile we will take a look at the upper half and find the middle or median of that upper half and that's going to be our upper quartile so it's going to be that 50 so our upper quartile is 50. once we have all of that information we can find the interquartile range we take our upper quartile and subtract the lower quartile so our upper is 50. minus our lower which is 32 so 50 minus 32 gives us an interquartile range of 18. so i'm going to draw some lines within our data to help us visualize exactly what this all means so our median was 38. so let's draw a line there now remember when we find quartiles we're splitting our data into quarters or four equal parts and our interquartile range is the range of that middle 50 percent so our lower quartile is 32 let's draw a line there and then our upper quartile is 50. so you can see that we have our quarters or four equal parts there what we do when we take a look at the interquartile range is look at this section here our middle 50 percent so we found the range or difference between 50 and 32 our upper quartile and lower quartile so that gave us that interquartile range let's move on to number two and do another example so for our second example we're going to have a data set with 10 numbers so remember the first thing we want to do is put the data in order from least to greatest this data is in order as well just like the first one so we can move to the second step which is find the median now that means the middle in the case of this number we have 10 numbers in our data set so we're going to break it in half the midpoint so we have five numbers on the left and five numbers on the right so our median is going to be right here between 8 and 11. it's between two numbers there so how we find the middle we need to find the average of 8 and 11 and that's going to be our median so we can do that by adding 8 plus 11 and then divide by two so eight plus eleven is nineteen and nineteen divided by two is nine and five tenths or nine and a half so that's our median let's do our lower quartile next so we need to take a look at the bottom half here the bottom five numbers and find the middle or median we have five numbers so we need two on the left and 2 on the right that leaves us with 6 in the middle so that's our lower quartile let's take a look at our upper quartile now so the upper 5 numbers the upper half 2 on the left 2 on the right that leaves us with 14 as our middle number or median there and that's going to be our upper quartile so 14. now we find the interquartile range so take the upper quartile and subtract the lower quartile so 14 minus six that gives us an interquartile range of eight now let's break this down and draw some lines to show our quartiles within the data to really help us understand both quartiles and interquartile range so the median was the middle right here the lower quartile is 6 so right here and the upper quartile is going to be 14. which is right here so we can see that we have our four equal parts now interquartile range we're taking a look at this middle 50 percent so the range of that the upper quartile minus the lower quartile and that gives us that interquartile range so there you have it there's how you find the interquartile range if you need more help with quartiles i'll add links to my other videos down in the description so i hope that helped thanks so much for watching until next time peace