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## Statistics and probability

### Course: Statistics and probability > Unit 1

Lesson 1: Analyzing one categorical variable- Identifying individuals, variables and categorical variables in a data set
- Individuals, variables, and categorical & quantitative data
- Reading pictographs
- Read picture graphs (multi-step problems)
- Reading bar graphs
- Reading bar graphs: Harry Potter
- Creating a bar graph
- Create bar graphs
- Reading bar charts: comparing two sets of data
- Read bar graphs (2-step problems)
- Reading bar charts: putting it together with central tendency
- Reading pie graphs (circle graphs)
- Picture graphs (pictographs) review
- Bar graphs review

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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.

## Want to join the conversation?

- what is median?(65 votes)
- A median is the number in the middle of a set of numbers. Sometimes, though, a group of numbers doesn't have one middle number. That happens when there is an even amount of numbers. To find the median you add the two middle numbers and divide by two.

Example: If you have 2,7,8,10, the median would be 7+8 divided by 2, which equals 7.5(101 votes)

- whats the difference between range and midrange?(20 votes)
- Avin, Great question!

A**range**is the difference between the lowest and highest values of the data set. For example, if the data set was 5, 8, 2, and 9; the lowest value would be 2 and the highest would be 9. You could also write it as 2 - 9.

The**midrange**is the mean (another word for average, in case you didn't know) of the maximum and minimum (lowest and highest) values of the data set.

So if the data set was 5,7,6,9 then the maximum value would be 9 and the minimum would be 5. To find the average of 5 and 9 would be to add them and divide by 2.

9 + 5 = 14

14 / 2 = 7

7 would be the midrange of this example .

As you can see, range and midrange are two totally different things, and now you know the difference!

Hope this helps! :)(51 votes)

- Is there a faster way of getting averages than adding all of them and dividing?(18 votes)
- There isn't a general way with random data that's simpler, but there are sometimes tricks with certain data. If all your numbers are identical (like
`4 4 4 4 4 4`

, then there's no need to add and divide - the answer is simply that number, in this case`4`

.

If you had`4 4 1 4 4 4 4`

, instead of adding everything, you could do`4*6+1`

and then divide, to be a little easier.

If you have an odd-count linear sequence of numbers, like`3 4 5 6 7 8 9 10 11`

then the answer is just the average of the lowest and highest numbers, in this case`3+11/2 = 7`

so the average is just`7`

.(6 votes)

- i need help what is the range :((5 votes)
- The range is the difference between the lowest and highest values. For example, if the data set was: 3,6,11,9,2; the highest number would be 11 and the lowest would be 2 and you would subtract those to get 9. You could also write it as 2-11.(12 votes)

- what is a mean(3 votes)
- It's s/a where s=sum of the numbers and a= amount of the numbers. So 3,4,5 would be 12/3 or 4/1 which is 4. Hope this helps!(7 votes)

- what is median and midrange.(3 votes)
- the medain is the middle # the midrange is the middle part of a range(2 votes)

- In what situation (IRL) would the mean or range of something come in handy?(4 votes)
- What is the purpose of finding the midrange? it seems a kind of useless concept to me(2 votes)
- it helps to find the average, median, and mean easier later down the line. it also allows people to see where things are average.(3 votes)

- Is Midterm and final the same thing?(2 votes)
- The midterm is halfway through the semester/term, and the final is at the end of the semester/term.(3 votes)

- What if you have two Modes?(2 votes)
- If there are two modes, find the mean of the two modes. (add them and then divide by two).(3 votes)

## 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.