welcome to another lesson in this lesson we're going to look at the lower quartile upper quartile and range lower quartile is the lower quarter of the data but first remember what's the most important thing always arrange the values from smallest to biggest so i'm going to do that quickly like that now the lower quartile it's it's the middle of the lowest middle okay so let's quickly explain what i mean by that so let's find the middle number what do we call that do you remember from the previous lesson well that's called the median so let's find the median first so we can cross off that cross that one off cross that one off that one that one that one that one that one and there's the middle so now that we have the middle let's ignore that one now we can look at this lower half and we'll call that the upper half now what number is halfway or what number is the middle number in this half well if we cross there across there oh now we stuck with two numbers all you do is you add those two numbers together and then you divide by two so that's going to give us four and a half so we can say that q1 which stands for the lower quarter or lower quartile is 4.5 if we look at the upper quarter well that's we crossed that one across that one and then we stuck with 7 and 11. so what we do is we add them together so we say 7 plus 11 and we divide the answer by 2 and that's going to give us 9 so q3 which we can also call the upper quartile is equal to 9. so we've just divided our data into quarters so this number here or over there divides it into two halves and then this number over here divides the lower half into a half and then this number over here which is between the 7 and 11 divides the data into or divides the upper half in half as well so what we have is we've just cut the data there we've cut the data there and we've cut the data there so we've got three quarters 1 two three four okay so that's where we get the word quarter from then the next thing i want to talk about is the range now range is your highest value minus your lowest value so your highest value is 12 and your lowest value is three so the range is going to be 12 minus three which is nine something else i want to talk about is is there a more mathematical way to do lower quarter and upper quarter yes there is so when we looked at the previous lesson we said that to find the median which is the one in the halfway position we could say n plus one divided by two so to find quarters we say n plus 1 divided by 4 and n is the number of values that you have which in this case is 9 so we say 9 plus 1 divided by 4 which is going to give us 2.5 that is not the answer that is the position that you should go to so you go to position number one position number two and then position two and a half is going to be exactly in between the four and the five and that's how we got 4.5 okay kevin now how do we find the third quarter well you still say n plus one over four but you take whatever that answer is and you multiply it by three because we're looking for the third quarter so that's going to be three times we said that this part becomes 2.5 and three times two point five is seven point five that is not the answer you must go to position seven point five so we go to position number one two three four five six seven the 11 would be eight so seven and a half is exactly in between seven and eleven so you add the seven and eleven together and you divide them by two and that is how we got the value of nine so we can say that the answer there is nine so the upper quarter is nine the lower quarter is four and a half the middle value is six and then the range the range is nine then the last thing they might want to ask you to work out the inter quartile range your teacher might call it the iqr that's easy it's the range of the quartile values so it's q3 minus q1 so that's going to be 9 minus 4.5 which is equal to 4.5