Main content

## 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

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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.

## 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.