THOTH

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

1/1/2011

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

Chapter 1

Index Numbers

Price Relative

𝑃 = 𝑝1

𝑝0 𝑋 100

p1 = price in current year

p0 = price in base year

To be expressed in the form of a percentage.

Simple Un-weighted Price Index Numbers

1. Simple average of relatives:

i. Un-weighted Arithmetic Mean

𝑃01 = 𝑃

𝑛

P denotes ‘price relative’

ii. Un-weighted Geometric Mean

𝑃01 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 𝑙𝑜𝑔𝑃

𝑛

2. Simple aggregative index number

𝑃01 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑒𝑎𝑟 𝑡𝑜𝑡𝑎𝑙

𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟 𝑡𝑜𝑡𝑎𝑙 𝑋 100

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

Weighted Price Index Numbers

1. Weighted Average of Relatives

i. The weighted arithmetic mean is

𝑃01 = 𝑤𝑃

𝑤

ii. The weighted geometric mean is

𝑃01 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 𝑤𝑙𝑜𝑔𝑃

𝑤

2. Weighted Aggregative Index Numbers

i. Laspeyre’s Price Index Number

𝑃01 = 𝑝1𝑞0

𝑝0𝑞0 𝑋 100

ii. Paasche’s Price Index Number

𝑃01 = 𝑝1𝑞1

𝑝0𝑞1 𝑋 100

iii. Marshall Edgeworth Price Index Number

𝑃01 = 𝑝1𝑞0 + 𝑝1𝑞1

𝑝0𝑞0 + 𝑝0𝑞1 𝑋 100

iv. Dorbish Bowley Price Index Number

𝑃01 =1

2 𝑝1𝑞0

𝑝0𝑞0+

𝑝1𝑞1

𝑝0𝑞1

𝑋 100

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

v. Fisher’s Price Index Number

𝑃01 = 𝑝1𝑞0

𝑝0𝑞0𝑋

𝑝1𝑞1

𝑝0𝑞1

𝑋 100

vi. Laspeyre’s Quantity Index Number

𝑄01 = 𝑞1𝑝0

𝑞0𝑝0 𝑋 100

vii. Paasche’s Quantity Index Number

𝑄01 = 𝑞1𝑝1

𝑞0𝑝1 𝑋 100

viii. Marshall Edgeworth Quantity Index Number

𝑄01 = 𝑞1𝑝0

𝑞0𝑝0

+ 𝑞1𝑝1

+ 𝑞0𝑝1 𝑋 100

ix. Dorbish Bowley Quantity Index Number

𝑄01 =1

2 𝑞1𝑝0

𝑞0𝑝0+

𝑞1𝑝1

𝑞0𝑝1

𝑋 100

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

x. Fisher’s Quantity Index Number

𝑄01 = 𝑞1𝑝0

𝑞0𝑝0𝑋

𝑞1𝑝1

𝑞0𝑝1

𝑋 100

Statistics – 2 Formula Book

For 2nd PUC Students

Vipin Srinath

Tests for an Index Number

1. Time Reversal Test (TRT)

𝑃01𝑋 𝑃10 = 1

P01 and P10 are expressed as mere ratios. Time reversal test is not satisfied by

Laspeyre’s, Paasche’s and Dorbish Bowley Index numbers. It is satisfied by only

Marshall Edgeworth and Fisher’s Index Number.

2. Factor Reversal Test (FRT)

𝑃01𝑋 𝑄01 = 𝑝1𝑞1

𝑝0𝑞0

P01 and Q10 are expressed as mere ratios. Time reversal test is not satisfied by

Laspeyre’s, Paasche’s, and Marshall Edgeworth and Dorbish Bowley Index numbers.

It is satisfied by only Fisher’s Index Number.

Consumer Price Index Number (Cost of Living Index Number)

1. Aggregative Expenditure Method

𝑃01 = 𝑇𝑜𝑡𝑎𝑙 𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑒𝑎𝑟

𝑇𝑜𝑡𝑎𝑙 𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑖𝑛 𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟 𝑋 100

Or

𝑃01 = 𝑝1𝑞0

𝑝0𝑞0 𝑋 100

2. Family Budget Method

𝑃01 = 𝑤𝑃

𝑤