Statistic Notes For Third Year B.com.

Master Index 1) 2) 3) 4)

Methods of calculating Index number:............................... 1 (Index No.)Time Reversal Test : .................................... 1 (Index No.)Factor Reversal Test : .................................. 1 Cost of living /Consumer’s price index no. ........................... 1

5) Conversion of fixed base to chain base index no. .................. 1 6) Conversion of chain base to fixed base index no. .................. 1 7) method of correlation. ................................................ 2

1) Methods of calculating Index number:  Laspeyre’s Method:

 Paasche’s Method:

 Fisher’s Method: F =

SO, F=

 Dorbish & Bowley’s Method:

So,

 Marshall-Edgeworth’s Method:

2) (Index No.)Time Reversal Test:  In this test for all methods just interchanging 0 and 1 & the formula is P01 X P10 = 1 For example Laspeyre’s method: P01 = After interchanging for time reversal test P10 =

So, P01 X

P10 =

X

≠ 1 So this method not satisfy the time reversal test.

3) (Index No.)Factor Reversal Test:  In this test for all methods just interchanging P and Q & the formula is For example Laspeyre’s method:

P01 X Q10 =

P01 =

After interchanging for factor reversal test

Q01 =

SO, P01 X

Q10 =

≠

So this method not satisfy the factor reversal test.

4) Method of cost of living index no./consumer’s price index no.  Aggregate Expenditure method: Index Number

I=

(in this formula the base year quantity is taken as weight.

But if the current year quantity has to taken as weight then the formula is Index Number

I=

 Family Budget Method: Index Number I =

Where I = price relative of each commodity =

W = weight = P0Q0

5) Converting fixed base index no. into chain base index numbers.



X 100

6) Converting chain base index no. into fixed base index numbers.



1|P a g e

7) Methods of correlation:  Scatter diagram method: This is a very simple method of studying the relationship between two variables. In this method one variable is taken on X axis & the other variable is taken on Y axis & for each pair of values, points are plotted on the graph paper. The diagram formed by the points on the graph paper is known as Scatter diagram. Looking to the distribution of points in the scatter diagram we can know the direction of the relationship & also get a rough idea about the degree of the relationship between the variables. If the point of the scatter diagram lie on one straight line is an increasing order, as shown in fig. 1, the correlation between the two variables is perfect positive. It the points of the scatter diagram lie on one straight line in a decreasing order as shown in fig. 2 the correlation between the two variables is perfect negative. If the points of the scatter diagram are not in one straight line but lie more or less around some straight line, the correlation between two variables is partial. If the point show an increasing trend, the correlation is partial positive, while if they show a decreasing trend, the correlation is partial negative. If the points are more close to a line, they exhibit high degree of relationship between the two variables. If the points of the scatter diagram are distributed haphazardly or randomly they exhibit absence of the relationship between two variables. Two such variables are linearly independent. Thus scatter diagram method is the easiest method of studying the relationship between two variables. The direction & to some extent the degree of relationship between two variables can be judged merely by seeing the scatter diagram. Merits of Scatter diagram method: This is a simple method of studying correlation between two variables. More mathematical knowledge is not required in this method. If one of the pairs of values is extreme, it does not influence much in deriving the conclusion. It is the first step in studying the relationship between two variables. Limitations of Scatter Diagram method: This method gives an idea about the direction & to some extent the degree of relationship between the variables, but does not give the exact measure of the relationship between the variables.  Karl Pearson’s Product moment method: This method given by the Karl Pearson is most accurate & it is very widely used. By this method the amount of relationship between two variables can be numerically measured. The numerical measure of correlation between two variables is known as correlation coefficient & it is denoted by “r”.

Where, So, r =

& Sx = or

r=

& Sy =

-

-Shortcut method of correlation --

 Spearman’s Method of Rank correlation: Where, d= difference in rank & n= no. of pairs formula is

but, When observation are paired the

where m = no. of times an item. 2|P a g e