Worked example: Creating a box plot (even number of data points)

represent the following data using a box a box and whiskers plot once again exclude the median when computing the quartiles and they gave us a bunch of data points and it says if it helps you might drag the numbers around which I will do because that will be useful they say the order isn't checked in that's because I'm doing this on the on Khan Academy exercises up here at the top right where you can't see there's actually a check answer so I encourage you to use the exercises yourself but let's just use this as an example so the first thing if I'm going to do a box and whiskers I'm going to order these numbers so let me order these numbers from least to greatest so let's see there is a one here and we've got some twos we've got some twos here and some threes some threes some five one four then fives I have a six I have a seven of a couple of eights and I have a ten so there you go I have ordered these numbers from least to greatest and now well just like that I can plot the the whiskers because I see the range my lowest number is one so my lowest number is one my largest number is ten so the whiskers help me visualize the range now let me think about the median of my data set is so my median here is going to be let's see I have one two three four five six seven eight nine 10 11 12 13 14 numbers since I have an even number of numbers the middle two numbers are going to help define my median because there's no one middle number I might say I might say this number right over here this 4 but notice there's 1 2 3 4 5 6 7 above it and there's only 1 2 3 4 5 6 below it same thing would have been true for this 5 so this does 4 & 5 the middle is actually in between these two so when you have an even number of numbers like this you take the middle two numbers this 4 and this 5 and you take the mean of the two so the mean of 4 & 5 is going to be 4 and 1/2 so that's going to be the median of our entire data set 4 and 1/2 4 and a half and now I want to figure out the median of the bottom half of numbers and the top half of numbers and here they say exclude the median of course I'm going to clewd the new median it's not even included in our in our data points right here because our media is 4.5 so now let's take this bottom half of numbers let's take this bottom half of numbers right over here and find the middle so this is a bottom seven numbers and so the median of those is going to be the one which has three on either side so it's going to be this two right over here so that right over there is the kind of the left boundary of our box and then for the right boundary we need to figure out the middle of our top half of numbers remember four and five where our middle two numbers our median is right in between at four and a half so our top half of a number starts at this five and goes to this ten seven numbers the middle one is going to have three on both sides the seven has three to the left remember of the top half and three to the right and so the seven is though I guess you could say the right side of our box and we're done we've constructed our box and whisker plot which helps us visualize the entire range but also you could say the middle roughly the middle half of our numbers