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in this chart right here we're giving out scores on midterm and final exams where the vertical axis is the score in points and then each of these pairs of bar charts give us for an individual where the blue bar is for example how a'shawn did on the midterm the yellow is how he did on the final for Emily the blue is how they she did on the midterm yellow is how she did on the final and we have a bunch of interesting questions here the first question what was the median what was the median score for the final exam so just as a review median literally means what was the middle score so really we should list all the scores for the final exam and sort them in order and then figure out what the middle score actually was so let's look at all the scores on final exam so scores scores on the final exam so you have a hundred here you shot and got a hundred on the final exam remember this yellow bar is the final exam so there's a hundred Emily also got a hundred on the final exam looks like it was an easy final exam Daniel also got 100 on the final exam and then let's see Jessica looks like she got a seventy-five seventy-five and then William got an eighty so if we were to sort these in order and let's say we did an increasing order you could you could write well the lowest score was a seventy-five then you have an eighty and then you have three hundreds 100 another hundred and another hundred so there's five scores right over here so you will have a middle if you had an even number then you would take the mean of the two Center of the two Center values but here you have one Center value and you when you order it like this it's pretty clear that your center value your middle value is 100 so the median score for the final exam is 100 and that's because you had so many hundreds here that the median the middle score was still a hundred what is the mid-range the mid-range of the midterm scores I'll do it in blue in honor of the color of the bars for the midterm so the mid-range is the mean of your highest and lowest scores so let's calculate this so let's go to the mid-range the mid-range you could view it as the arithmetic mean or the the average of your highest and lowest scores so the mid-range of mid term of mid term so let's see the highest midterm score looking at the blue the highest one is right here so Jessica I've got 100 on the midterm so that's your highest score your lowest score on the midterm looks like this one right over here Daniel got a 60 got a 60 and so the mid-range is going to be the mean the arithmetic mean of these two numbers so you add 100 plus 60 divided by 2 you get 160 over 2 or 80 so this right over here is going to be 80 what was the average student score for the final exam well for that we just have to add up the scores on the final exams and then divide by the number of scores we have so we might be able to do that in our heads let's see well we can do we just write it over here so we have 100 plus 100 plus 100 plus 75 plus 80 so all of that divided by all of that divided by 5 that'll give us our average if someone tells you average without giving more information they're probably talking about the arithmetic mean so this is going to be 300 plus let's see 300 plus another 155 so it's going to be 450 5 over 5 this is equal to 450 5 over 5 and let's see 5 this is going to be equal to 5 goes in let me write it down here this is equal to 5 goes into 45 or 450 90 times and into 5 1 so this is going to be equal to 91 so the average score for the final exam is a 91 what was the mode for the final exam scores so the mode is the most common score so once again we've listed all of them and it's pretty clear that the most common score here is 100 100 shows up three times while 75 only shows up ones and an 80 only shows up once so here the most common score is 100 it shows up 3 times what is the range of the midterm scores so the range is literally the difference between the high score and the lowest score so the high score we already figured up and this is for the midterm for the midterm so the highest score is 100 and we're going to subtract from that the lowest score which was a 60 so the range is equal to 40 the mid-range was the average of these two things the range is just the difference between the two so the range of the midterm scores is is 40 and we're done