in this video we're going to talk about how to make box and whisker plots now what you need to be able to do is you need to be able to identify five key data points in your data set the first two are very straightforward it's the minimum and the maximum now the other three data points are the first quartile the second quartile and the third quartile now once you have that you can plot those things on a number line and then draw the box in whisker plot around that so let me show you an example so you could see how this is going to work so let's say we have the numbers 11 22 20 14 29 and then 8 35 27 13 49 10 24 and 17. so first let's determine the three quartiles in addition to the minimum and the maximum the first step is to arrange the numbers in ascendant order so the lowest number that we have here is 8 and then 10 and then 11. now let's cross out those numbers the next number is 13 and then 14 and then 17. after 17 we have 20 22 24 and 27 after that is 29 which we can see it here 35 and then 49. so at this point we have a total of 13 numbers in our list now the first thing is to break the data into two equal parts so let's calculate q2 which is the median of the entire data set so if we eliminate the first two numbers on both sides and then if we keep doing that until we get the middle number this will give us the median which is 20. now what i'm going to do is i'm going to draw a line and then put 20 on top so this is the second quartile so now i have two equal parts of data i have six numbers on the left side and six numbers on the right side now i need to find the median of the lower half of the data so if i eliminate the first two and the last two i mean the next two i have two numbers in the middle so the median is going to be the average of those two numbers the average of 11 and 13 is 12. so this is q1 the first quartile now the median will be between these two numbers that is the median of the upper half of the data so the average of 27 and 29 is 28 so that's q3 the third quartile so we have q1 q2 and q3 now the next thing we need to do is identify the minimum value and the maximum value the minimum value is the lowest value in the data set which is eight and the maximum value is the highest value in the data set which is 49. now we need to check to make sure that these two values are not outliers because if they're outliers they're not going to be part of the box and whisker plot they will exist outside of that now what we need to do is we need to determine a range of numbers in which the outliers can't be so it's going to be q1 minus 1.5 times the iqr value to q3 plus 1.5 times the iqr value so any number that is outside of this range that is part of the data set is an outlier now the iqr value the interquartile range is basically the difference between q3 and q1 so q3 is 28 q1 is 12. so the interquartile range is 16. so using this interval it's going to be q1 which is 12 minus 1.5 times 16 and then q3 is 28 plus 1.5 times 16. now let's get a calculator and plug these numbers in so 12 minus 1.5 times 16 that's going to be negative 12 and then 28 plus 1.5 times 16 that's 52. so negative i mean not negative 8 but 8 is in this range so 8 is not an outlier it is the minimum of the data set 49 is also between negative 12 and 52 so 49 is not an outlier so now that we know we don't have any outliers at this point we can draw the box plot or the box in whisker plot let's begin by creating a number line the lowest value is 8 and the highest is 49 so let's start from zero and let's go by tens until we get up to 50. so first let's plot q1 q1 is 12 which is approximately right there and then q3 is 28 which is just under 30. and then draw a rectangle now q2 is 20 so we're going to put a line here so as you can see this is q1 q2 and q3 now our next step is to plot the minimum which is around 8 so there it is and then the maximum is at 49. so we're going to put a line just below 50. and so that is the box and whisker plot that corresponds to the data set that we see here so that's how you can draw it but now what about if we had an outlier how would that impact the box and whisker plot so let's consider an example in which that's the case so first let's write out a list of numbers let's say we have the numbers 18 34 76 29 15 41 46 25 54 38 20 32 43 and then 22. so if you think you know what to do feel free to pause the video and try it so let's begin by putting the numbers in ascendant order so we have 15 18 20 and so here are those numbers and then after 20 it's 22 and then 25 and then 29 after 29 it's 32 34 38 and 41 and then after that it's going to be 43 46 54 and then the last one is 76. so we have a total of let's see this is 3 6 9 12 14 numbers so we want to split it into two equal parts let's put a line between the seventh and the eighth number so we got seven numbers on the left side seven numbers on the right side so the median is going to be the average of those two numbers the average of 32 and 34 is 33. so this is the second quartile now we need to determine the median of these seven numbers which is going to be the middle number 22 but let's replace 22 with a line so we can split the left side into two equal parts of three numbers but i'm going to put 22 on top so you can see that it represents q1 the median of the left side of the data now 43 is the middle number of these seven numbers so let's do the same thing let's replace 43 with a line and so this is going to be the third quartile and we'll put 43 on top so keep in mind the quartiles they divide the data into four equal parts so we have four equal parts of three numbers now i'm going to put a comma between 46 and 54 so it doesn't look like 4 654. our next step is to calculate the interquartile range so it's q3 minus q1 so it's the difference between those two values so it's 43 minus 22 which is 21. so that's our iqr value and excuse me our next step is to see if we have any outliers so first let's calculate the range in which no outliers should exist so q1 is 22 and iqr is 21. q3 is 43. 22 minus 1.5 times 21 and that is equal to negative 9.5 and then 43 plus 1.5 times 21 is 74.5 now are there any numbers in our list of numbers that is not in this range 15 is in this range but 76 is not so therefore 76 is an outlier so we can't include that in the box and whisker plot 76 will be outside of it and so now we can plot the box and whisker plot so let's start with the number line so let's go up to 80. so this is going to be zero we're going to say 80 is over here so this is 40 and this is 20 and 60. and in between are 10 30 50 and 70. so let's start with q1 q1 is 22 which is just above 20 and q2 i mean q3 is 43 so that's gonna be to the right of 40. so this is just a rough estimate now q2 is 33 which we're going to put here so this is q1 q2 q3 now our minimum value that is not an outlier is 15. the highest value that is not an outlier is 54. so we're going to plot those two numbers 15 is right between 10 and 20 and then 54 is almost in the middle between 50 and 60 but a little bit close to 50. and so this is the minimum and this is the maximum that is not an outlier now to show the outlier all we need to do is basically put a point at 76 which should be somewhere around here and that's basically it so that's how you can show the outlier that exists basically outside of the box and whisker plot thanks for watching