Statistics & Histogram Bars - Mathematics, Class 9 Video Lecture

ooh that looks like a nasty cold I think
she may need an antihistamine and an e
oh wait not a nanny this is the lesson
on histograms not antihistamines sorry
about that let me see if I can fix it
there there that's better okay we're
gonna talk about statistics today and
we're gonna talk about histograms
statistics is just the tool that helps
us understand data
it helps us organize data understand the
data and then communicate that
understanding other people and today
we're gonna be talking about one
statistical tool or actually two we're
gonna talk about histograms and bar
graphs let's look at an example I've got
a data set on the board here that shows
the age of students at public school 322
maybe you can see I've got two columns
I got a column with the age and months
and these rain these are ranges of
months and then I got a column with
numbers or frequencies or the counts and
what this means is that for the age
range 120 months to 130 months there
were 16 students at public school 322
and there were 60 students at public
school 322 that fell into the range 130
240 months
well that that chart that table tells us
a lot but I think statistics would allow
us to understand this better and if we
apply two histogram to this maybe you'd
communicate to this information more
easily to people that wanted to
understand what you were doing so let's
build a histogram to build a histogram I
have to start
with two axes and I've got a vertical
axis here or the y axes and along that
I've labeled it the number of students
and then I've got an x axis or
horizontal axes and I've labeled that
age ranges and I've also labeled the
whole chart age of students at public
school 322 and that's kind of important
because you want this table or this
chart or this histogram to be
self-explanatory you want someone to be
able to look at this and say oh I know
what that charts telling me so it's
important to label the chart we need to
label your axes too and this horizontal
axis was the age ranges of the students
and it corresponds to the information in
that that left-hand column so let's put
that information on to the chart I've
got 120 to 130 in this region 130 140
and so forth now I need to fill in this
number line and right now there's kind
of nonsense numbers in there what I need
are numbers that will handle this data
and the lowest number in this data the
lowest frequency is 16 and the largest
frequency is 60 so I got to go up to a
number at least as big as 60 so I can
get all these data points along there
well let's do that and I've gone up to
70 well then the next trick is for each
of these ranges I want to build a bar
that goes up to the spot on the vertical
number line that corresponds to the
correct frequency for 130 I went up to
60 because 130 to 140 there was a
frequency of 60 now there's two
additional things I want to tell you
about this this particular statistical
tool
first of all this is a histogram
it's a histogram and not a bar chart
because I've got numbers along the
horizontal axis if I had classes of
things like Chevrolet Toyota Nissan
Cadillac then it would be a bar chart
second thing I want you to notice is
that this is a continuous range of
numbers it starts at 120 and it ends at
190 and there's no number between 120
and 190 that I can't fit into one of
these categories so this is a continuous
range and because it's a continuous
range I run my bars right up into each
other so they touch each other if there
were a gap between these bars it might
imply to someone that there was a gap in
the numbers and there isn't it's a
continuous range of numbers so my bars
are continuous without gaps
well let's look at another data table in
this data table I have assembled
information about the hair color of
students at public school 322 and it
reads just like the last table I've got
two columns the left column is listing
hair color and the right column is
listening frequency or count and you
read it the same way there are 23
students at public school 322 that have
red hair and there's 61 students at
public school 322 that have black hair
now we can create a chart to help us
understand this data and I've done that
along the bottom I've got the classes or
categories that were in the left column
red hair brown hair black hair gray hair
must've been a teacher blond hair and
then along the vertical axes I've got a
range that's big enough to handle from
my smallest number to my largest number
and then I painted the bars so they go
up to the frequency that corresponds
with that class red was about 23 now is
this a histogram or a bar graph well
these are not numbers these are classes
of things and for it to be a histogram
these have to be numbers so this is a
bar chart
another thing red to blonde is not a
continuous range their groups or
categories and there's there's no
implication that there's a continuous
flow between red and blonde this is not
a continuous flow these are distinct
separate categories and because of that
I put a gap between them well there's
some other things we can learn from
histogram and we're going to show you
that now I've got another table here
with data on it but I put in different
data points the frequency within 120 to
130 months was 70 and there were 69
between 130 to 140
well if I build a histogram of this new
data it looks like this and you'll
notice that there's a lot more high
values on the left side than there is on
the right side the right sides kind of
low values the left sides kind of high
values the numbers are really skewed in
that direction skew just means they're
pushed over in that direction or we have
higher values or lower values on one
side or the other and we call this a
skewed distribution here's another data
table and you'll see that the values are
low at the top and high at the bottom or
excuse me low at the top high in the
middle and low at the bottom and when I
create a histogram for that it looks
like a normal or a bell curve low at the
outsides high at the insides and we call
that a normal distribution
another data table and then this one the
counts are pretty much high at the top
high at the bottom but lower in the
middle my histogram shows that I've got
high values at the top high values at
the bottom and in the middle I've got
lower values so there's two high areas
on the histogram and to or by we call
this a bimodal distribution now on this
distribution the counts are all pretty
much the same they're all it's kind of a
flat line that would tie those together
and it looks kind of like a flat line
distribution and we call it a flat
distribution
now you try this one hit the pause
button do the problem and then hit the
forward key to move on to the answer
we're asked to chart this data now the
first question we want to ask is should
we be building a histogram or a bar
chart
you remember histograms got numbers
usually continuous along the horizontal
or the x axis and a bar graphs got
classes or categories of things along
the horizontal axis well these are
categories of things or categories of
cities so I think what we want is a bar
graph not a histogram and that's what it
would look like I'd have these
categories or the city names along the
horizontal axis I build the bar up to
the level of the frequency for that that
class like asteroid has 467 people so
the bar goes up a little bit under 500
and I've left gaps between the bars
because asteroid to West moon is not any
kind of a continuous flow is there an
outlier well yeah an outlier stands out
real real well on a bar graph or a
histogram you can see that star is a
whole much a whole lot higher bar than
any of the other bars so star is an
outlier
well we've conducted a survey of people
to ask them how many friends they had on
Facebook and we broke up the responses
into ranges zero to twenty five friends
on Facebook 25 to 50 friends 50 to 75
and so forth and then we listed the
frequency of the counts in this right
hand column so there are 18 people who
had between 0 and 25 friends now we want
to create a chart to describe this
should we create a histogram or a bar
graph well these are numbers and they go
from 0 continuously to 125 so what we
wants a histogram and when we build it
it would look just like that I hope
yours looks like this - now does this
bar graph or this histogram describe a
particular type of distribution well you
see it's low at the 0 and 25 left hand
side and it's low on the high end at 125
and it goes up to higher values in the
middle so if we were to draw a curve and
it looked a little bit like a bell and
we call that a bell curve and we call
this distribution a normal distribution
well we we didn't learn much about
antihistamines today but I hope you
learned a little bit about histograms
and bar graphs now let's test that
knowledge go to WWE and download the
worksheet on histograms after you've
done the worksheet then go back to
master math and try the quiz on
histograms and be sure to come back and
see us again real soon