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## Analyzing one categorical variable

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# Reading bar charts: putting it together with central tendency

## 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.