Statistical series, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com

hello children today we continue again
with the chapter frequency distribution
in the previous lecture I told you about
the classification of data or how to
classify the data in a proper systematic
order for particular statistical
analysis now this classification of data
leads to further step that is the
statistical series that means the
classified data has to be arranged in a
proper statistical Series form so that
analysis can be made easily now let us
see how statistical series are formed
before starting the formation of
statistical series I will just want to
make it clear to you the meaning of the
statistical series here the statical
series means a systematic arrangement of
items into a particular order or
sequence in different classified that
agrees as I told you earlier when we
classify the data then you have to
classify the data into different groups
according to their qualities or
attributes similarly a systematic
arrangement of items this is a
systematic arrangement of items into a
particular order or sequence in
different classified categories that
means the category is what you have
formed with the help of classification
of data those categories are again
arranged in a particular systematic
order to form the series okay so this
means that is statistical series is
again a further step after the classic
classic occasion of data that means
forming the different particular order
of sequence for further analysis now let
us go to further this clarification that
what are different types of statistical
series because the data what you
collect that is of different types so
again according to your particular
purpose of inquiry or according to the
type of data what you are collected you
have three different type of series this
is individual series discrete series and
continuous series these are three
different types now one individual
series that is on the basis of
individual unit whereas discrete and
continuous series that is on the basis
of frequency you must remember you must
be knowing that or you remember very
well that what is meant by frequency
frequency means the number of times an
item appears in a series so accordingly
when we are making the series on the
basis of individual unit then we are
taking into consideration each and every
individual unit and not the frequency of
any unit this is known as individual
series and when we are considering the
frequency that means how many times a
particular item has appeared in the
series or in the data then this is
called frequency series now for further
explanation I will give you an example
now in the case of individual series
when we are making the individual series
then here first we'll take the serial
number and suppose we are taking the
marks of students in the class then when
we are noting down the marks of each and
every student then this will be the case
of individual series then suppose they
are 10 students in a class 6 7 8 9 now
let us take this example here I have
made two columns serial number and marks
and for our example I have taken marks
in this case that is marks of ten
students scoring in particular subject
now it can be marks it can be another
any other variable you can take like
income of people
or expenditure of different group of
people or you can say the age or height
of children in the class whatever but
here we have taken the marks that does
not mean that only marks can be
categorized like this it can be any
other variable now suppose we are taking
marks of ten students the class then
each and every child is taken into
consideration it may be in the form of
one two three four five six like this or
you can note down the names of the
children and these other marks for one
child has scored twenty another has
scored 25 third one has scored ten like
this marks of all ten students are given
here this is the case of individual
series because individual items are
taken into consideration and remember
again that suppose two children have
scored thirty there in that case here
you will not note down the marks in the
typed in the form of frequency you will
write down the marks in individual units
whether the number is repeated or not so
don't remember do not convert it into
type of frequency because this is the
case of individual series right now we
come to the next type of series that is
on the basis of frequency this will take
how the frequencies are written down
against the different type of variables
now there are two type of variables
discrete variables and continuous
variables as I told you in the previous
lecture variable means the item which
varies which can be measured in units
and which varies with time now two type
of variables are their discrete
variables and continuous variables now
we take the example of this discrete
variable and continuous variables
discrete variables as I told you earlier
discrete variables are the variables
which are
given incomplete numbers they cannot be
expressed in fractions whereas
continuous variables they are expressed
in fractions or they can be in the form
of class interval or so now first we'll
take the discrete series now how we form
the discrete series this is the case of
individual series right individual
series here we are taking the discrete
series now here in the discrete series
as I told you this is on the basis of
frequency distribution so you will make
the columns accordingly first you right
now the marks first row first column and
second is frequency these are always
made on the basis of frequency now marks
suppose you have noted down that mark
distribution twenty to thirty
thirty-five forty like this then the
frequency of these masks suppose five
children have scored ten marks twenty
marks have been scored by two twenty two
have been scored by four thirty have
been scored by it five thirty five by
two and these are six so this type of
distribution is called discrete series
the total number of students in this
case is five to seven eleven five
sixteen sixteen eighteen and twenty-four
okay so this type of distribution is
known as discrete series which is always
the marks cannot be or any description
is given in the full numbers it cannot
be given in fractions or it cannot be
given in the form of class interval
right now we come to the third one that
is continuous series
so these are three type of series 1 you
have taken individual unit and
individual series discrete sees now we
come to the third one that is continuous
series this can be given in the form of
fractions it can be given in the form of
class interval also now let us take it
in the form of class interval now
suppose you are taking the box of
students you want to divide then minimum
marks at 5 then 1 class interval is 5 to
10 second will be these are marks and
again the frequency or number of
students you can say number of students
I am writing down here that means it is
a same as frequency 5 to 10 10 to 15 15
to 20 20 to 25 suppose you are taking
only 5 that means highest marks are 30
and minimum marks of 5 now we have to
see how many students are in this
category suppose there are 4 10 to 15
how many have score suppose they are 2
this is 5 then 6 or whatsoever right
that makes total
right so this way when we make the
series then this is known as individual
continuous and discrete series this is
known as statistical series in three
different forms now after understanding
all this let us come to another
description that is what is meant by
class there are certain terms which you
will require to know when you are making
the continuous series or discrete series
or maybe individual series but normally
these terms are used in the form of
class interval or continuous series now
what is the class as I told you this is
the marks here these are in the form of
class interval when I say class then
what does it mean what is a class that
means a class represents a range of
particular value here this is a class
this is five to ten this is a particular
class that means the range of marks is
between five to ten that means children
are scoring marks not less than five and
not more than ten in this category we
have four students second class is ten
to 15 that means minimum marks are ten
maximum are fifteen this is another
class so class represents a range of
value and each given interval is called
a class right so number of classes when
we are deciding here I have taken five
classes now another step is we have to
decide how many classes you are going to
take when you are compacting the data
now suppose you have collected the data
which is ranging from zero to hundred
then you can take the class interval of
10 or maybe 20 because keep this in mind
when you are dividing the data into
different class intervals or different
classes then these classes should be
between
five two either five or maximum twenty
right why I say that class should be
between five and twenty normally we take
this number why because if you take this
class distribution less than 5 then
description will not be very clear or
analysis cannot be made very clearly for
clear comparison or analysis at least
five class intervals should be given and
if you take more than twenty then will
be too complicated to analyze because
then there will be lot of description or
lot of class intervals which will give a
detailed analysis and that will be it
will complicate it now you must be
thinking that suppose there are thousand
children a thousand data regarding
thousand people you are collecting now
how to give the data in five class
intervals or twenty for that you have to
decide that what class interval you are
taking or how many number of classes
will decide on the basis of this thing
that number of classes number of classes
are R upon I now what is our here R is
the range that means what is the range
of data and how do we decide the range
this is the minimum number or minimum
the lowest data or and another side the
highest data the difference between the
lowest and highest data gives you the
range suppose your date collected the
data which is ranging between 0 to 1000
that in this case your range is 1000 if
it is ranging between 0 to 50 here the
range is only 50 so accordingly
whatever is the range and accordingly
you take the class interval
as I told you suppose they are 500
children in a particular locality and
you are doing the investigation of 500
children then if you want five classes
then the class interval you will take
how much 500 divided by the class
interval that is 100 you will take and
the number of classes will be five right
so five classes for this you'll number
of classes will become five when you
take the class interval of 100 if there
are five thousand then you can take the
class interval of 1000 now if you want
to make more than five classes then you
can make the class interval of you can
say if you want to make twenty classes
then how much now here suppose you want
to take the class interval of two
hundred or you can say twenty five two
five zero then you will get the class
interval of twenty number of classes 20
and class level will be 250 so this way
the classes are decided on the basis of
the range now next is another term what
is class interval now how do you define
the class interval range of the class is
called
class interval in this case the range is
five to ten so class interval or the gap
between the two is five in the other way
suppose you are taking here this with
this example the class interval is 1000
in this class interval is 50 so this way
the difference between the upper limit
and the lower limit so class interval
you can say is upper limit
upper limit minus lower limit that is
class interval this is or you can say l2
minus l1 l2 is the upper limit and l1 is
the lower limit so in 10 to 20 the class
interval will be 10 in 10 to 15 the
class interval because upper limit is 15
lower limit is 10 that is 15 minus 10
that is 5 okay so class interval is the
difference between the upper limit and
the lower limit this upper limit and the
lower limit is also known as class limit
so one concept what you have learnt is
that is first is class what is a class
second is class interval
third is class limit this is known as
class limit so class you have understood
here how to divide the class class
interval is the difference between this
and class limit is the upper limit minus
the lower limit that is known as class
limit if this limit can be either in
whole number or it can be in fractions
also maybe five point five to ten point
five or ten point five to fifteen point
five like this okay so this is known as
class limit another term what you are
concerned here is that is mid value what
is made value mid value now what is
meant by mid value mid means middle so
middle value now when we are talking
about class interval of ten to twenty
suppose now what will be the middle
value over here this will be here in
this case mid value will be equal to 10
plus twenty upon two this is equal to
thirty upon two that is fifteen so what
is the mid value the lower limit plus
the upper limit as I told you what is
limit the lowest the lower side is lower
limit this
you