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## Statistics and probability

### Course: Statistics and probability > Unit 2

Lesson 1: Displaying quantitative data with graphs- Representing data
- Frequency tables & dot plots
- Creating frequency tables
- Creating dot plots
- Reading dot plots & frequency tables
- Dot plots and frequency tables review
- Creating a histogram
- Histograms
- Interpreting a histogram
- Create histograms
- Read histograms
- Histograms review
- Stem-and-leaf plots
- Reading stem and leaf plots
- Reading stem and leaf plots
- Stem and leaf plots review

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# Histograms

Here's how we make a histogram:
1. Collect your data and decide on the number and size of bins (categories) you want to divide your data into.
2. Count the number of data points that fall within each bin.
3. Draw a graph with the bins as the x-axis and the frequency counts as the y-axis.
4. Draw vertical bars to represent the frequency count for each bin. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

- Why do you call it a histogram? What does it mean, and what base word does it come from.(17 votes)
- in a histogram, when you skip a #, aren't you supposed to draw a break where the # skipped is? Why doesn't Sal do that(5 votes)
- He didn't actually skip the 5, he just put it there and didn't draw a bar, or u could think of it as drawing a bar with a height of 0.(7 votes)

- Does it have to be number frequency to differ from a bar graph? Wouldn't it be a histogram if you chart population? (# of Mexicans, #of African Americans, # of Asians, etc.)(2 votes)
- i don't think this is a clear representation of a histogram. this is more of a bar graph- a histogram is meant to have frequency density on the y axis (or so i've been taught). i want to know how to read a real histogram with frequency density on the y axis and measurement on the x axis can anyone point me in the right direction? thanks in advance(7 votes)

- here, so that one day i can prove my teacher wrong.(4 votes)
- Isn't what Sal drew a bar chart and not a histogram because:

a) Histograms should group numbers into ranges?

b) Histograms are supposed to have have "frequency density" not frequency as the y axis?

If it is not so then could someone please explain why and what actually is a histogram (and the difference from a bar chart)?(1 vote)- No, because histograms measure quantitative data (numbers or ranges of numbers) and bar graphs measure categorical data (such as favorite colors). Also, the bars on histograms have no spaces between them, while the bars on bar graphs do, and the bars on bar graphs can be rearranged and still make sense.(6 votes)

- histograms and bar graphs are not the same histograms are joined while bargraphs have spaces between the data(3 votes)
- The buckets are the groups of the different numbers: The 1 bucket, the 2 bucket, and so on(0 votes)

- How would you do this if you had all decimal numbers... For example, 1.2, 1.9, 5.6, 3.2, etc. I am confused, and my school work does not explain this very well.

Could some one please explain?(4 votes)- I am pretty sure that you work that out the same way, just with decimals(0 votes)

- I have to do a histogram for a group of data, and my survey question is "What is your favorite movie genre?" and my options were action, horror, adventure, fantasy, comedy, and romance. The results where:

action- 15

horror- 10

adventure- 6

fantasy-5

comedy- 19

romance- 5

My problem is that I have no idea how to do a histogram that can portray this information.(2 votes)- You would draw a histogram like in the video where the bottom would be the type of movie (action, horror, etc), and the left side would be numbers. Then draw bars to reflect the result for each type of movie.

Hope this helps.(4 votes)

- how do you create a frequency table and a histogram if you have 50 numbers? (Ex.1943,1950,1951)(3 votes)
- The same way it is done in the video starting at @0:45.

Read your list of numbers one at a time and, for each number you read, add +1 to the corresponding counter. After having counted the number of occurrences of each number, you can divide by the total number of numbers to obtain their frequency.(2 votes)

- Hmmm Histogram looks a lot like a Bar graph(3 votes)

## Video transcript

In this video we're going to
talk about another way of visualizing data called the
histogram, which is a very fancy word for a not
so fancy thing. I think it's probably fair to
say that the histogram is the most used way of representing
statistical data. Let me just show you how to
figure out a histogram for some data, and I think you're
going to get the point pretty easily. So I have some data
here and I want to represent it with a histogram. What we're going to see
is how frequent are each of these numbers. And in order to figure that
out, let me just write the numbers down, let me just
categorize them in their respective buckets. So I have a 1 here. I have a 4, so I want to leave
space for the 2, the 3, and put a 4 there. I have a 2. I have a 1. Let me put that 1 on a stack
right above that 1. I have a 0-- let me put the
0 to the left of the 1. I want to put them in order. I have a 2, another 2. Let me stack that above
my first 2. I have another 1. Let me stack that above
my other two 1's. I have another 0. Let me stack it there. I have another 1. Then I have another 2. Another 1. I have two more 0's. 0, 0. I have two more 2's. I have a 3. I have two more 1's. Another 3. And then I have a 6. So no 5's, and then
I have a 6. And that space right there
was unnecessary. But right here I've listed--
I've just rewritten those numbers and I've essentially
categorized them. Now what I want to do is
calculate how many of each of these numbers we have. So
let me go down here. So I want to look at
the frequency of each of these numbers. So I have one, two,
three, four 0's. I have one, two, three, four,
five, six, seven 1's. I have one, two, three,
four, five 2's. I have one, two 3's. I have one 4, and one 6. So we could write it this way. We could write the number,
and then we can have the frequency. So I have the numbers 0, 1, 2,
3, 4-- we could even throw 5 in there, although 5 has
a frequency of 0. And we have a 6. So the 0 showed up four times
in this data set. 1 showed up seven times
in this data set. 2 showed up five times, 3 showed
up to two times, 4 showed up one time, 5 didn't
show up, and 6 showed up one time. All I did is I counted this
data set, and I did this first. But you could say how
many times do I see a 0? I see it one, two, three,
four times. How many times do I see a 1? One, two, three, four, five,
six, seven times. That's what we mean
by frequency. Now a histogram is really just
a plot, kind of a bar graph, plotting the frequency of
each of these numbers. It's going to look a lot
like this original thing that I drew. So let me draw some axes here. So the different buckets
here are the numbers. And that worked out because
we're dealing with very clean integers that tend to repeat. If you're dealing with things
that the exact number doesn't repeat, oftentimes people
will put the numbers into buckets or ranges. But here they fit into
nice little buckets. You have the numbers 0,
1, 2, 3, 4, 5, and 6. This is the actual numbers. And then on the vertical
axis we're going to plot the frequency. So one, two, three, four,
five, six, seven. So that's 7, 6, 5, 4, 3, 2, 1. So 0 shows up four times. So we'll draw a little
bar graph here. 0 shows up four times. Draw it just like that. 0 shows up four times. That is that information
right there. 1 shows up seven times. So I'll do a little bar graph. 1 shows up seven times. Just like that. I want to make it a little bit
straighter than that-- 1 shows up seven times. 2-- I'll do it in a different
color-- 2 shows up five times. Do a bar graph, go all
the way up to five. 2 shows up five times. 3 shows up two times. We have one 3, two 3's. 4 shows up one time here. 5 doesn't show up at all. So it doesn't even get
any height there. And then finally, 6
shows up one time. So I'll do 6 showing
up one time. What I just plotted here,
this is a histogram. This right here is
a histogram. Very fancy word, but I think you
will agree it's a fairly simple idea. Figure out the frequency of each
of these numbers and then plot the frequency of each of
these numbers and you get yourself a histogram.