The document discusses index numbers which measure changes in variables over time. It defines simple and composite index numbers. The three main types of index numbers are price, quantity, and value indexes. Examples are provided to demonstrate calculating price indexes using the fixed base method. Index numbers are calculated for different years using different base periods to compare price changes.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
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2. Definition:
An index number measure the changes in a variable or a group of
variable with respect to time.
Simple Index Number:
A simple index is based on a single commodity.
Composite Index Number:
A composite index is based on several commodities.
Types of Index Numbers:
There are three types of index numbers.

3. (i) Price Index Number:
It compares levels of prices from one period to another.
(ii) Quantity Index Number:
A quantity index measures how much quantity of a variable
changes over time.
(iii) Value Index Number:
The value index measures changes in total monetary worth. It
measures changes in rupee value of a variable. In effect, the
value index combines price and quantity changes to present a
more informative index.

4. Example – 1:
The price of rice in Karachi per kg is Rs. 150 in the year 2013 and
the price of rice per kg was 120 in the year 2012.
Find index number for the year 2013 and comment.
100
2012inicePr
2013inicePr

100
120
150

Solution:
Price in 2012 = Rs. 120
Price in 2013 = Rs. 150
Price Index =
=
Price Index = 125 %
The index number 125% means that the price of rice per kg has
increased by 25% in 2013 as compared to 2012.

5. Year 1990 1991 1992 1993 1994 1995 1996 1997
Price
(Rs.)
45 50 60 65 70 72 68 83
Method of Computation of Simple Index Number by
Fixed Base Method:
Example – 2:
The following data shows the prices of an item for 8 years.
Calculate the Index number of all the years taking 1990 as the base year.

6. Year Price
Price Relative =
1990 45
1991 50
1992 60
1993 65
1994 70
1995 72
1996 68
1997 83
100
P
P
o
n

100100
45
45

11.111100
45
50

33.133100
45
60

44.144100
45
65

55.155100
45
70

160100
45
72

11.151100
45
68

44.184100
45
83

Solution:

7. Year 1990 1991 1992 1993 1994 1995 1996 1997
Price
(Rs.)
45 50 60 65 70 72 68 83
Example – 3:
The following data shows the prices of an item for 8 years.
Calculate the index number of all the years taking average
Of 1990 to 1993 as base year.

8. Year Price
1990 45
1991 50
1992 60
1993 65
1994 70
1995 72
1996 68
1997 83
81.81100
55
45

91.90100
55
50

09.109100
55
60

18.118100
55
65

27.127100
55
70

91.130100
55
72

64.123100
55
68

91.150100
55
83

Solution:

9. Years 2001 2002 2003 2004 2005 2006 2007 2008 2009
Prices 12.5 15 17 20 25 22.5 27.5 37.5 35
Years 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Prices 65 72 75 76 80 85 82 88 88 90 95
Years 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Prices 10.75 12.1 13.1 13.85 14.25 15.9 16.8 14.15 13.2 14 10.75
DO YOURSELF
1. Find price relatives for the data given below using:
(i) 2001 as base
(ii) 2007 as base
2. Compute the index number from the following average wholesale prices of
cotton taking 2000 = 100.
3. Find the index number of prices from the following data:
(a) using the average of last five years as base
(b) using the average of 1998 to 1999

10. Answers
1).(i)100,120,136,160,200,180,220,300,280.
(ii)45.45,54.55,61.82,72.73,90.91,81.82,100,136.36,127.27
2).100,110.77,115.38,116.92,123.08,130.77,126.15,135.38,135.38,138.46,146.15
3).(a)78.01,87.81,95.07,100.51,103.41,115.38,121.92,102.69,95.79,101.60,78.01
(b)94.05,105.86,114.61,121.17,124.67,139.11,146.98,123.79,115.49,122.48,94.05