Bowley’s Coefficient of Skewness, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com

welcome to eco holux in this video we
will learn about how to calculate bonus
coefficient of skewness so in the
previous video we have learned about how
to calculate quartiles and we were
discussing about quartile deviation so
we were aware we were aware about how to
calculate Q 1 and the Q 3 so the same
lines ball is coefficient of skewness is
based on the value of quartiles if the
if the series or the items are a
symmetrical the value of Q 3 and the
Kuban are equidistance when we compare
to the value of the median if the series
is asymmetrical it means it considered
as a series consider as I skewed series
so in that series the Q 3 the value of Q
3 is a further than the or the above
then the value of median and now the
same line the value of Q 1 is below the
value of median if we consider about the
how positively skewed or the negatively
skewed if the distribution is positively
skewed it means the value of Q 3 is
further from the value of median and the
Q 1 is also not in the equidistance with
the value of median so this is just a
brief background of how to calculate
this coefficient of skewness given by
polish so here we will solve for the
practical question that is how to
calculate the Polish coefficient of
skewness so this is the continuous
series given and the frequency given to
you so the first step as usual we will
write the formula so formula for ballast
is penis that is we are referring SK as
a skewness and B for the name borders q3
plus q1 minus 2 median divided by q3
minus q1 this is the formula to
calculate the coefficient of skewness so
here the first of all we will learn
about how to calculate these quartiles
so the demand of the formula is to
calculate 3 items that is first is q1 q3
and the value of median
so yeah we'll start with the value of a
Cuban so Cuban is that is an by for but
in order to get the value and we have to
calculate cumulative frequency from the
series so the next column is of
cumulative frequency if you want to
learn how to calculate cumulative
frequency it can refer to the previous
videos here with the help of calculator
we are now calculating the cumulative
frequency so 12 12 plus 16 is 28 28 plus
26 is 54 54 plus 38 is 92 92 plus 22 is
114 114 plus 15 is 129 129 plus 7 is 136
and last is plus 4 that is 140 so here
we can write at that 114 the total of
this that is summation F is 140 so the
cumulative frequency here we will
calculate n by 4 means of 140 divided by
4 so here it comes out as 35 now we have
to look for the data that is that
consider the 35th idea so the thirty
fifth item falls under this category
it means 35 item is less than 54 that is
why we are taking this series so in
order to calculate Cuban or know the
exact value of Q 1 because we have now
assured that 35 30 falls under this
category it means the value of Q 1
should be between 20 and 30 in order to
know the exact value of the Cuban we
have to apply the formula that is L 1
plus n by 4 minus DF upon F multiplied
by 5 here plus sign again put here
now l1 is the lower limit so this is the
class we are referring this is the class
so no limit is 20 plus n by 4 is 35 here
the trick is cumulative frequency we are
taking cumulative frequency of the just
that previous one it means here the
previous one is between d8 now talking
about F frequency of the same
distribution that is 26 so 26 multiplied
by I is the class interval so here the
class interval gap is 10 so we can solve
this question this equation very easily
35-28 comes out at 7 so 7 upon 286 into
10 7/26 that is 20 plus 0.26 input 10 so
here 20 plus 2 point 6 so the value of Q
1 is 22 point 6
this is the value of Q 1 so here in the
corner we can write Q 1 is a 22 point 6
this is the value of Q 1 now we have to
calculate the Q 3
so the value of q 3 that is 3 and by 4
so here 3 into 140 divided by so that
comes out as 1 0 5 it means 1 0 5th item
will be or not q 3 so 1 0 5 will fall
under this value that is 1 0 5 400 140
so in the column of cumulative frequency
we are putting a bracket just to give a
representation on that
so for Q 3 know the exact value between
40 and 50 so we have to apply the
formula same formula l1 + 3 n by 4 minus
CF divided by F into PI so here L 1 the
lower limit of this class is 40 + 3 n by
4 is 1 0 5 - cumulative frequency of the
previous class that is preceding class
that is 92 here the value of F is 22 the
frequency and multiplied by the class
interval so 1 0 5
- 90 - comes out as 30 so 40 plus 13
upon 22 into 10 13 divided by 22 comes
out this 0.5 9 multiplied by 10 so here
40 + 5.9 it means 45.9 is the value of Q
three forty five point nine so here in
the corner q3 45.9 we are writing now
for the last value of the demand of the
formula that is median we have to
calculate the median median is very
simple we just have to calculate n by
two
here and by 2
140 divided 2 is 70 so now you have to
look into the disk you ability frequency
the column of cumulative frequency not
the value of the seventieth I dropped
false so you can write 1770 the item
falls under this category so now to know
the exact value of million we have to
apply the formula so here the lower
limit is 30 30 plus n by 2 is 70 minus
CF of the preceding class CF of the
preceding classes 54 divided by F the
frequency of the same class that is 38
multiplied by 10 here were solving at
this equation that is 70-54 so third p
plus 16 upon 38 x 1016 upon 38 comes out
this 30 plus 0.4 to 1 to 10 so again we
can write a 30 plus 4 point 2 so the
value of million I am writing on the
hour that is thirty four point two is
the value of the median so here the
value of median is thirty four point now
we have all these three values now we
just have to put these values into the
formula of skewness and now we get the
answer
so yeah
bonus coefficient of skewness q3 the
value of Q 3 is 40
sorry forty five point nine forty five
point nine plus the value of Q 1 is
twenty two point six minus two median
that is two into the value of median
thirty four point two divided by q3
minus q1 that is forty five point nine
minus twenty three point six so there's
a simple equation we have to solve this
forty five point nine plus twenty two
point six that comes out as sixty eight
point five minus thirty four point two
into two there is 68 24 when we multiply
these two figure figure comes out at
this so here forty five point nine minus
twenty two point six so that is twenty
three point three now we are just
removing this bracket sixty eight point
five a minus sixty eight point four and
that is 0.1 divided by twenty three
point three so zero point 1 divided by
twenty three point three so the figure
comes out this zero point zero zero so
this is your answer final answer hope
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