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Reading bar charts: putting it together with central tendency

Let's combine some learning! Here we looking at bar charts and using the information to determine the measures of central tendency. Created by Sal Khan.

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Video transcript

In this chart right here we're given 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 Ishaan did on the midterm, the yellow is how he did on the final. For Emily, the blue is how 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 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. Sp you have 100 here. Ishaan got 100 on the final exam. Remember, this yellow bar is the final exam. So there's 100. Emily also got 100 on the final exam. It looks like it was an easy final exam. Daniel also got 100 on the final exam. And then, let's see, Jessica, it looks like she got a 75. And then William got an 80. So if we were to sort these in order, and let's say we did it in increasing order, you could write-- well, the lowest score was a 75, then you have an 80, and then you have three 100's-- 100, another 100, and another 100. 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 values. But here you have one center value, and 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 100. What is the midrange of the midterm scores? I'll do it in blue in honor of the color of the bars for the midterm. So the midrange is the mean of your highest and lowest scores. So let's calculate this. So let's go to the midrange. The midrange, you could view it as the arithmetic mean, or the average of your highest and lowest scores, so the midrange of midterm. So let's see, the highest midterm score, looking at the blue, the highest one is right here. So Jessica 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. And so the midrange is going to be the mean, the arithmetic mean of these two numbers. So you add 100 plus 60, divide 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 could-- let me just write it over here. So we have 100, plus 100, plus 100, plus 75, plus 80. So all of that divided by 5, that will 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 another 155, so it's going to be 455 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 ninety times and into 5 once. 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 the most common score here is 100. 100 shows up three times, while a 75 only shows up once, and an 80 only shows up once. So here the most common score is 100. It shows up three times. What is the range of the midterm scores? So the range is literally the difference between the highest score and the lowest score. So the highest score, we already figured out, and this is 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 midrange was the average of these two things. The range is just the difference between the two. So the range of the midterm scores is 40. And we're done.