Quantity Index Numbers, Business Mathematics and Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

okay so we're in the video now on retail
price indices and index numbers and
chain base index numbers and weighted
index numbers so hopefully this will
give some ideas of what to do first
thing we do need to know that is some
formulas so let's have a reminder about
what the formulas are so the basic idea
of an index number is to find the index
number we take the current price we
divide it by the base year price and
then we times it by 100 if we want a
chain base
index number
then we take the current price
/ the previous year's price
times a hundred and everyone's awaited
index number
they're going to take the sum of the
waiting's times the index numbers or the
mean index numbers divided by the sum of
the waiting's I'll go through an example
of using each of these formulas so that
you can see how they work but the basic
idea of an index number is it is a
number so for example if you're given an
index number say 107 what is index
number is telling you is that there's a
7% increase it's over the hundred
compared to the base year now the base
year could be ten years ago twenty years
ago five years ago last year but it's
basically telling you that there's been
a change so a 7% increase compared to
the base year now if the index number
will say equal to 82 then again it's a
comparison to a base year somewhere in
the past this time it's less than 100 so
it's showing that there's a decrease so
this one would be an 18% decrease
so let's have a look at some of the
ideas so here's an example question so
talking about some raw materials and
they want to work out the index numbers
for 2004 and 2008 relative to 2000 so
what they're telling you here is that
this is the base year so the rustic
price indices so we think about the
formula so the formula was the index
number equals the current price divided
by the base year
for us
times a hundred so for 2004
the current price was three pound and
five the base year price was two pound
60 and when there are times that by 100
to get the index number so
we have 5/8 my six times 100 equals so
one hundred and seventeen point three
wouldn't go much more accurate than that
and quite often just round to the
nearest whole number to get a feel for
what's going on but I'm going to leave
it at under seventeen point three notice
I don't for the percent sign an index
number is what it is it's a number and 4
2008 we can see that the current price
was three pounds forty one the original
base year price was sixty times that by
100 to get the index number so three
point zero one
define my tip 96 times 100 equals so 131
points to zero on decimal place 731
going to 2 again no % just index number
fashion goes on to say that the raw
materials cost in the base year of 2006
m8 no how much would it cost to the same
amount of materials 2004 so here's where
we're going to actually use the index
number to use a price so we've got 6800
and we're going to times that by the
index number as a decimal so we can see
how the increase has changed so the
index number 117 so as a decimal
it's one point one seven
so we have 6,800
times one point wants them so seven
thousand nine hundred and fifty six
pounds so that's the basic concept of an
index number using the formula and
finding out some index numbers this one
meaning there was a seventeen point
three percent increase this one meaning
that there was a thirty one point two
percent increase here I just used the
two decimal first place figure I could
have times by one point one seven three
either of those answers would have been
acceptable as long as I show you a
method so so look at another example
so here we've got an example of chain
base index numbers so we've got some
membership values for a club and we want
to find out the chain base index numbers
as the years move from 2006 to 2009 so
their difference here between the
ordinary investment per formula it's the
same base you use the previous year
always as your base year so for 2006
we're going to be using the current
membership one five nine one divided by
the previous year's membership one four
three four times that by 100 and that
will give us our first index number
/ home for 3-4 times 500 so 110 point 9
and for 2007 it's going to be the
current membership divided by the
previous year's management room a chain
basis always going comparison to the
previous year so they've won five nine
100 so we got 116 1 5 9 1 times 100
so 101.9
from 2008 president membership 1 4 3 7 /
the previous year so I won 61 times 100
so 1 4 3 7 / 160 180 equals times 100
equals seven eighty eight point six and
four
2009-present membership / previous
membership times 108 divided by 4.2
so those are the chain based index
numbers for this club and we can see
that for 2006 and 2007 the numbers were
up over hundreds there was a slight
increase in the membership of 2008 there
was a number below 100 so there was a
drop here so it's a decrease in
membership and in 2009 there was a
increase in membership compared to the
previous year because it's a comparison
to previous year in chambers index
numbers which year saw the biggest
percentage change in membership when I
saw below so 10% dropped by 901 yeah
there's a big change there so there are
twelve eleven percent drop so it was 11
percent drop here so 2007 to 2008 so
which year saw the Beast interchange
membership 2008 there was nearly eleven
point four percent decrease that was the
largest change
okay temp Center increase 1% increase
1.9 percent increase folks an increase
this was an eleven point four decrease
so that was the biggest percentage
change okay so that's an example of
chain base and last example then we're
going to look at a weighted Price Index
for the materials we've got to look at
the formula for weightings so we have
the weighted index
is equal to the sum of the waiting's
times the index numbers divided by the
sum of the weightings so the proportion
here are the waiting for each of the
categories and the index numbers are
given we might have to calculate those
the could be of tape or keeping with two
prices and we've got a calculated items
themselves but in this particular
example they've given them already
so our weighted index then is going to
be the waiting times the index number
and there's a some off so let's keep
adding a beach motion so we got 10 times
136 plus 35 times 121 plus 25 times 95
and it's divided by the sum of all the
waiting's these are percentages lively
chatter 200 we'll just check thirty
forty seventy five eighty hundred yen so
divided by hundred so calculated that
should follow the bit much principle so
just type it as we see it hundred
fifteen plus ten times hundred and
thirty-six plus thirty five times
hundred twenty-one plus 25 times ninety
five equals and divided by 100 equals so
one hundred and fourteen point so that's
how weighted index number so what is the
percentage change in the ROM sale price
over these eight years
well this increase of fourteen point two
percent and there's all your examples of
index numbers