Construction of a Frequency Distribution, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com

[Music]
hi we are going to construct a frequency
distribution with this raw data in this
data just so that we can use it as we
move along is a collection of 40 pennies
so in 99 a class of students collected
40 pennies and then they wrote down the
year of each of these pennies and so
we're going to organize these 40 data
values into a frequency distribution
first thing that you want to kind of
decide when you when you can start to
frequency distribution is the number of
classes that you want the number of
classes on your frequency distribution
and to to kind of get there we first
look at the range and then we kind of
think about the amount of data that we
have and how big we want these classes
to be and what their class width is so
we'll kind of go through that process
now so let's find the range the range is
the difference between the highest data
value and the smallest data value our
highest data value should be 99 and it
is because this was in 99 when we
collected the pennies and our lowest
value that's right here it's a 66 so we
have a range of 33 so as we think about
how many classes that we want we want to
keep in mind that we don't want to
spread them out too much and have you
know 20 classes for a range of 33 that
would become a silly there wouldn't be
much data in each class maybe just one
one or two pieces of data but we also
don't want to get too small we don't
want three classes and then then they
get all collected into those three
classes and we don't see the significant
shape of the data either so but most of
the time we want a number of classes
between 5 and 15 is kind of a rule we
can bend it but that's kind of the the
role that we deal with when we construct
a frequency distribution and then for
the data that you guys are going to be
analyzing in this class you're probably
going to stick around
5 6 7
maybe up to ten but probably not I tried
a few things I tried six and seven and I
landed on seven pretty quickly because
when I took 33 and divide it by 7 this
is how you find the class width which is
the next thing you want to do so this is
to find the class width you take the
range and you divide it by the number of
classes that you want when I did seven I
got four point seven one and a class
width we've had a ceiling function on
this and the ceiling means to round up
the value to the nearest whole number
always round it up so even if this was
four point zero one we would still round
it up to five okay and I like a class
width of five it's odd we like an odd
class width because then our midpoint is
a whole number it's it's a reasonable
value I like having five data values and
we just like the number five so I saw
that quickly and I was like seven
classes it is so six I think gave us a
four and so that was a little bit small
for a class width and it was an even
number so I went to seven and that was
that was what I decided on so keep in
mind our class width is five and we want
to start our class limits for our
frequency distribution so this is our
class limits
our frequency distribution also keeps up
with a tally I'll show you why we do
that in just a second and then our
frequency
okay our class limits always start with
our smallest data values so here it
would be a 66 our class width is 5 and
so the difference between 66 and our
next lower class limit is should be 5 so
66 plus 5 is 71 so that's going to be
our next lower class limit and the
reason why it's this way vertical and
not horizontal is because we our class
width is the number of data values that
are in that class the number of data no
data values but the number of numbers
that would land right there so 66 67 68
69 and 70 so that makes five and so
that's why this goes up to 70 all those
values 66 67 68 69 and 70 is going to
land right here and that's what our
class width is representative of so
that's why we're adding five vertically
as we come up with our class limit so
we'll keep on doing that until we get
seven classes so 76 which would make
this 75 81 which would make this 8086
ninety-one
96
and of course that is seven so now we
have seven classes and we of course just
add four to get to this last because
this would be a hundred and one if we
added five and so making this last class
limit upper class limit a hundred so you
can kind of go out down and check you
should be able to add five and get to
all these and difference between all
these should be five which they end in
five so that's nice
alright so frequency distribution just a
simple frequency distribution has the
class limits and then the frequencies
and so we using the tally column here
though just to make our life simpler and
it's how we arrange our data into this
so taking this raw data and arranging it
into this frequency distribution and I
think the best way to do this is just to
start right here with your first data
value and hitting Itali
where it lands so 96 of course it's
going to be right here and I'm just
gonna put a tally because that's where
it is then we'll move on to 98 and it
goes here 97 96 83 is gonna be our first
one in a different class it's gonna be
right here and we'll just keep doing
this for every data value and hitting
Itali
where it lands so stopped 83
all right so I just tallied up the data
got it into the frequency distribution
tallies here and now I can count up my
tallies and record my frequencies so the
tallies are just to get us to be able to
record our frequency count them up and
we get our frequencies okay so there's a
frequency distribution of this raw data
and now we can look at it and start
analyzing it so much easier now that we
can organize it and just this very
simple and easy way