[Music] welcome to math with Mr J in this video I'm going to cover how to read interpret and understand box and whisker plots so basically what are we looking at when it comes to box and whisker plots now keep in mind box and whisker plots are also called box plots so in this video we're going to cover the basics now at first box in whisker plots may look complex and not make any sense but it's just a matter of understanding what you're looking at and what box and whisker plots represent now simply put box and whisker plots are a way to display data and the spread of that data they give us a visual let's jump into our example and see exactly how to read and interpret a box and whisker plot for our example we're going to be taking a look at years of teaching experience so 10 teachers were surveyed and here are the results again this is years of teaching experience this data is in order from least to greatest and the box and whisker plot has been created below now when it comes to box and whisker plots there are five key Parts they show us a five number summary of the data set box and whisker plots display the minimum the first quartile the median the third quartile and and the maximum let's start by taking a look at the minimum and the maximum so the minimum number of years of teaching experience is three the maximum is 18 so the minimum is 3 years and the maximum is 18 years so the minimum and maximum are just the smallest and largest numbers in value within the data set so as far as the box and whisker plot we have the minimum right here and the maximum right here so let's label this minimum and maximum so the whiskers that extend out from the rectangle extend to the minimum and to the maximum now that we covered the minimum and maximum we're actually going to move to the middle and we're going to take a look at this line right here inside the rectangle that line represents the median the median is the middle point of the data the halfway point or the 50th percentile the median is also referred to as the second quartile now since we have 10 numbers within the data set the halfway point is going to be in between the 8 and the 10 so this is is the median it splits the data set in half we have five numbers to the left and five numbers to the right now we are directly in between 8 and 10 so we take the average of those two numbers to find the median so we do 8 + 10 and then divide by 2 8 + 10 is 18 / 2 is 9 so the median is N9 now for this one we can just think that N9 is directly in between 8 and 10 but keep in mind whenever you have two numbers and you need to find the median in between you can take the average in order to do so so again the line inside the rectangle is the median so that's the halfway point within our data now we need to take a look at the first quartile also known as the lower quartile and then the third quartile also known as the upper quartile let's take a look at the first quartile first so we need to take a look at the bottom half of our data so right here now the first quartile is going to be the median or halfway point within our bottom half of the data so we have five numbers within that bottom half so this is going to be the median of the bottom half of the data that means means that's going to be the first quartile that's the 1/4 Mark within our data so the 25 percent Mark or 25th percentile so the first quartile is 7 that's represented by this part of the rectangle so this is the first quartile or lower quartile again it's seven now we need to find the third quartile so the upper quartile let's take a look at the upper half of our data we need to find the median so the midpoint of that upper half that's going to be right here so 12 12 is our upper quartile the third quartile that's the 34s mark within our data so the 75% Mark or 75th percentile so the third quartile is 12 and that is going to be this part of the rectangle so third quartile those are the five parts of a box and whisker plot we have the minimum which was three years of teaching experience so minimum was right here then we have the first quartile which was seven so right here then we have the median which was nine so right here then we have the third quartile which was 12 so right here and then we have the maximum which was 18 years of teaching experience which was right here box and whisker plots use quartiles so the data is split into four parts so fourths we have about 25% of the data right here we have about 25% of the data right here we have about 25% of the data right here and then we have about 25% of the data right here now the box within the box and whisker plot represents the inter quartile range so the middle 50% of the data and then a whisker extends to the minimum that's going to be the bottom 25% of the data and then the other whisker extends to the maximum that's going to be the upper 25% of the data now for one final recap I'm going to erase all of that writing on the box and whisker plot that way it's a little more clear as to what we're looking at now without all of that writing we can focus more on the box and whisker plot so one final recap here we have the minimum which is three represented right here then we have the first quartile which is represented right here and that is seven then we have the median which is represented right here and is nine then the third quartile is represented right here and that is 12 and then lastly we have the maximum which is 18 and represented right here so there you have it there is an over viw of how to read interpret and basically understand what you're looking at when it comes to box and whisker plots I hope that helped thanks so much for watching until next time peace