Frequency Distribution - Presentation of Data, Business Mathematics & Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

in this video let us look into the
frequency distribution let us see what
is frequency distribution and the
different types of frequency
distribution now the frequency table or
the frequency distribution is a method
to present raw data in the form from
which one can easily understand the
information contained in the raw data
now frequency distribution of two types
now the frequency distribution are of
two types
the first one is discrete frequency
distribution and the second one being
continuous grouped frequency
distribution now let us look into the
discrete frequency distribution
now let us look into the discrete
frequency distribution the process of
preparing this type of distribution is
very simple the construction of a
discrete frequency distribution from the
given raw data is done by the use of the
method of tally marks we've already seen
what this means in the previous videos
we just have to draw some bars that is
the vertical lines and when we draw four
of them we just need to draw the fifth
one across them and make it one group so
that means it is equal to 5 and then in
the next column say for example if it is
number of students then it is understood
that the number of students is 5 that is
corresponding to that strike across
tally marks in the first column of the
frequency table we write all the
possible values of the variable from the
lowest to the highest if we compare the
last sentence to the previous videos
when we looked into or when we did the
grouping of raw data we we did come
across the term variate and we linked it
to the marks because the marks were
differing that is it was varying one
three five eight thirty nine twenty
three twenty one and so on so that's
what this means in the first column of
the frequency table we write all the
possible values of the variable form
from the lowest to the highest
so this is discrete frequency
distribution let me give you a quick
example for discrete frequency
distribution
so here a quick example of a discrete
frequency distribution the question here
or the data here is or the statistical
data you're given is the number of
children in 20 families are 1 1 2 3 4 3
2 1 1 4 5 2 4 2 2 1 3 3 2 5 so these are
the number of children and 20 different
families now let us construct a discrete
frequency distribution for this given
data
so here is the discrete frequency
distribution for the about statistical
data as explained in the previous sheet
the first column consists of the
variables from the lowest to the highest
order that is the number of children is
a varying thing here so the different
number of children the 20 families have
are one two three four and five but how
many families do have just one child so
we first have to count it in terms of
the tally bars we first count one and
then draw one vertical bar so this is
one the next one is one so we draw
another vertical bar the next one is
here we draw another vertical bar the
next one is here we do our vertical bar
the last one is here which is a five so
we cross the whole thing so this means
five which is mentioned here in the
frequency so similarly we do likewise
for now let us see the number of
families that have two children that is
one two three four five six so here we
are one two three four we cross the bar
that becomes five and then one more six
so here it is six so all we need to do
is write the variable in the first
column the bars in the second column and
the frequency in the third column so
this is how we construct a discrete
frequency distribution now the second
type of a frequency distribution is
continued or grouped frequency
distribution
let us go into that in the next sheet
now let us do understand what is
continuous or grouped frequency
distribution now in the previous sheets
of which had the method of condensing
the raw data is convenient only when the
values in the raw data are largely
repeating and the difference between the
greatest and the smallest observations
is not very large as you saw the last
time then the minimum number of children
were 1 and the maximum wave 5 so hardly
they were like 1 2 3 4 5 but when we
come to the continuous of the grouped
frequency distribution the difference
between the greatest and the smallest
observations are very large let us
quickly look into an example now let the
marks obtained by 30 students of a class
in test be thirty nine twenty five five
thirty three nineteen twenty one twelve
forty eight thirteen twenty-one nine one
ten eight twelve seventeen nineteen
seventeen forty one forty twelve forty
six 3717 27 36 to 23 and 19 now
arranging this in the discrete frequency
distribution is not very simple it does
not solve the purpose of making this
further simpler because the difference
between the lowest variable and the
largest variable is not very small so
this is when the continuous of the group
the frequency distribution comes into
play now let us see how we can arrange
these marks by the method of continuous
are grouped frequency distribution
now here we have the representation of
this given data in the method of
continuous are grouped frequency
distribution here what we're doing is
the different marks that is out of 50
varies from 0 to 10 although we do not
have 0 on this list that is how it is
there there is a possibility of somebody
scoring a 0 and also a 10 and also 30 40
and 50 and so on that is between 0 and
50 so we group the numbers between 0 and
50 in terms of 0 to 10 10 to 20 20 to 30
30 to 40 and 40 to 50 now we count the
tally bars or make the bars for the
number of marks that is between 0 and 10
between the mark 0 and 10 we've got 1 2
3
four five and six so between zero and
ten also includes ten now let me come to
this now if you consider the way we've
split this it is zero to ten and ten to
twenty
so what does it mean now where do we
write the marks of 10 do we write it in
the first row or the second row I am
coming to that in the forthcoming video
but sure if you see the number of
students that have got the marks between
zero to ten or six now let us count that
from here to is one six is two and then
we've got one is three and then five is
four and then 9 is 5 and 10 is 6 so here
it includes 10 now let's leave that now
for a little later and let us finish
this so this is how we write the bars
and then the number of students getting
the marks between 0 to 10 is 6 similarly
between 10 and 20 there are 11 students
as those have got the marks between 10
20 20 and 35 students 30 and 40 for
students 40 and 50 for students so this
is how the continuous are grouped
frequency distribution is constructed
now let me deconstruct the whole table
of continuous of the grouped frequency
distribution for you now these groups
the zero to ten ten to twenty of our
classes the class zero to ten means the
marks obtained between zero and ten
including zero and excluding ten this is
the most important point here it is
excluding ten the number of observations
falling in a particular class is called
the frequency of that class or class
frequency thus the class zero to ten has
a frequency of six and the class ten to
twenty has eleven as class frequency
the class zero to ten we say that the
zero is the lower limit and 10 is the
upper limit of the class similarly in
the class ten to twenty we say that 10
is the lower limit and 20 is the upper
limit so the span of the class that is
the difference between the upper limit
and the lower limit is known as the
class interval for example the class 10
to 20 in the class territory the class
interval is 20 minus 10 which is 10 so
that is called as a class interval now
there are two methods of classifying the
data according to the class intervals
that is exclusive method and inclusive
method
now let me quickly show you an example
to distinguish exclusive method earning
and enclose a method in the next sheet
and a quick clarification here I was
counting 10 for the class interval 0 to
10 but then it is not because if you see
we've got 5 year which is 1 and then
we've got 9 year which is to 1 which is
3
8 which is 4 6 which is 5 & 2 which is 6
so we are not including 10 in 0 to 10 so
so this is an example 4 exclusive method
anyways I will show you a clear
difference between the exclusive method
of class interval and they enclose a
method of class interval in the next
sheet
now here we have an example to
illustrate the differences between the
exclusion method and the inclusive
method of class intervals it is evident
from this example that both the
inclusive and exclusive methods give us
the same class frequency although the
class intervals are apparently different
in the two cases in this example in the
case of exclusive method the class
interval is 100 if you see whereas in
the case of inclusive method the class
interval is 99 that is thousand hundred
- thousand as a hundred and thousand 99
- thousand is a 99 however 99 is not the
correct class interval whenever the
inclusive method is used it is necessary
to make an adjustment to determine the
correct class intervals and to have
continuity so if a minus B is a class in
inclusive method then an exclusive
method it becomes a minus H by 2 minus b
plus h by 2 where H is equal to lower
limit of the class - upper limit of the
previous class divided by 2
so here if you can clearly see that in
the exclusion method the thousand one
hundred is not included in counting the
number of workers
so in the inclusive method it is very
clear that it is already mentioned only
2099 so this is the difference between
exclusive method and inclusive method
you