Index Number – MCQ -

Last Updated on: 18th June 2025, 03:18 pm

Index Number – MCQ

Statistical Sampling Theory – MCQ

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1. Laspeyres’s index is based on
(a) Base Year Quantities
(b) Current Year Quantities
(c) Average of base and current year
(d) All of the above.

Laspeyres’s index is based on Base year quantities.
So, Option (a) is correct

2. Chain base index Number shows
(a) Short Term Fluctuations
(b) Long term Fluctuation
(c) Market Rates
(d) None.

For determining short term fluctuations, chain base index number is used.
So, Option (a) is correct

3. In which method the current year quantities are taken as weights?
(a) Paaschee’s
(b) Laspeyre’s
(c) Bowley’s
(d) None.

In Paaschee’s Index number, current year quantities are taken as weights.
So, Option (a) is correct

4. Laspeyre’s formula for computation of price index numbers is
(a) $\displaystyle \sum{{}}$ p₁q₁/ $\displaystyle \sum{{}}$ p₀q₀ $\displaystyle \times$ 100
(b) $\displaystyle \sum{{}}$ p₁q₀/ $\displaystyle \sum{{}}$ p₀q₀ $\displaystyle \times$ 100
(c) $\displaystyle \sum{{}}$ p₁q/ $\displaystyle \sum{{}}$ p₀q $\displaystyle \times$ 100
(d) None of the above.

Laspeyre’s formula for computation of price index numbers is base year weights (quantity),
( $\displaystyle \sum{{}}$ p₁q₀/ $\displaystyle \sum{{}}$ p₀q₀) × 100
So, Option (b) is correct

5. What is the formula of Paasche’s index number
(a) $\displaystyle \sum{{}}$ P₁Q₀/ $\displaystyle \sum{{}}$ P₀Q₁
(b) $\displaystyle \sum{{}}$ P₁Q₁/ $\displaystyle \sum{{}}$ P₀Q₁ $\displaystyle \times$ 100
(c) $\displaystyle \sum{{}}$ P₁Q₀/ $\displaystyle \sum{{}}$ P₁Q₁
(d) All of the above.
Formula of Paasche’s index number is
( $\displaystyle \sum{{}}$ P₁Q₁)/( $\displaystyle \sum{{}}$ P₀Q₁) × 100
So, Option (b) is correct

6. Formula of chain index number is

(a) $\displaystyle \frac{{C.Y.\Pr ice}}{{\Pr ev.\Pr ice}}\times 100$

(b) $\displaystyle \frac{{C.Y.\Pr ice}}{{100}}\times P.Y.\Pr ice$

(d) All of the above.

Chain Index for Period k, relative to previous = (Price in Period k / Price in previous Period)*100
So, chain index number

= $\displaystyle \frac{{C.Y.\Pr ice}}{{P.Y.\Pr ice}}\times 100$

So, Option (a) is correct

7. Basis of factor reversal test is
(a) P₀₁ x P₁
(b) P₀₁ x Q₀₁
(c) P₁₀ x Q₀₁
(d) P₀₁ x Q₁₀ .
P₀₁ x Q₀₁ is the basis for factor reversal test.
It equals to total value ratio.
So, Option (b) is correct

8. Time reversal test is complete when
(a) P₀₁ x Q₀₁= 1
(b) P₀₁ x Q₁₀ = 1
(c) P₀₁ x Q₁₀ = $\displaystyle \sum{{}}$ p₁q₁/ $\displaystyle \sum{{}}$ p₀q₀
(d) P₀₁ x Q₀₁= $\displaystyle \sum{{}}$ p₁q₁/ $\displaystyle \sum{{}}$ p₀q₀
Time reversal test is complete when P₀₁ x Q₁₀ = 1
It shows reversibility in time.
So, Option (b) is correct

9. Circular test is satisfied by
(a) Laspeyre’s formula
(b) Paasche’s formula
(c) Bowley’s ideal formula
(d) None of the these.
Laspeyres, Paasche and Fisher’s indices fail to satisfy Circular test. Only the fixed weight aggregates method and simple aggregates method satisfy Circular test.
So, Option (d) is correct

10. Fishers Ideal index number satisfies
(a) Time Reversal Test only
(b) Factor Reversal Test only
(c) Both Time & Factor Reversal Test
(d) None of these.
Fishers Ideal index number satisfy both time Reversal Test as well as Factor Reversal Test.
So, Option (c) is correct

11. Fisher’s ideal formula does not satisfy
(a) Time reversal test
(b) Circular test
(c) Factor reversal test
(d) Unit test.
Fisher’s ideal formula satisfies Time reversal test, Factor reversal test and Unit test.
But, Fisher’s ideal formula does not satisfy Circular test.
So, Option (b) is correct

12. The most suitable average for index numbers is
(a) Mean
(b) Median
(c) Harmonic mean
(d) Geometric mean.
Geometric mean is the most accurate average for index numbers
So, Option (d) is correct

13. The consumer price index by simple aggregate method of the following, data $\displaystyle \sum{{}}$ P_o = 175, $\displaystyle \sum{{}}$ P₁ = 205 is :
(a) 117.142
(b) 102.92
(c) 112.92
(d) 132.92
Index number under simple aggregate
P₀₁ $\displaystyle \sum{{}}$ P₁/ $\displaystyle \sum{{}}$ P₀X100
Here $\displaystyle \sum{{}}$ P₁ = 205 $\displaystyle \sum{{}}$ P₀ = 175
P₀₁= (205 /175) x 100 = 117.142%
So, Option (a) is correct

14. Fisher’s index is________the mean of the Paasche’s and Lyspeyre’s index:
(a) Arithmetic
(b) Harmonic
(c) Geometric
(d) None of these
Fisher’s index = $\displaystyle \sqrt{{Laspeyre\text{ }\times \text{ }passche\text{ }\times \text{ }100}}$
which is the geometric mean of
Paasche’s and Lyspeyre’s index
So, Option (c) is correct

15. The price level of a country in a certain year has increased 30% over the base The index number is:
(a) 30
(b) 130
(c) 170
(d) None of the above 100
Base year index = 100
Price level increased 30%
Current year index = $\displaystyle 100\times \frac{{130}}{{100}}=130$
So, Option (b) is correct

16. The simple Aggregative formula and weighted aggregative formula satisfy
(a) Factor Reversal Test
(b) Circular Test
(c) Units Test
(d) None of these.
The simple Aggregative formula and weighted aggregative formula does not always satisfy Factor Reversal Test.
However, simple Aggregative formula and weighted aggregative formula always satisfy Circular Test.
So, Option (b) is correct

17. “Fisher’s idea index is the only formula which satisfies”
(a) Time Reversal Test
(b) Circular Test
(c) Factor Reversal Test
(d) None of these.
Fisher’s ideal Index is the only formula which satisfies Factor Reversal test.
So, Option (c) is correct

18. Purchasing Power of Money is
(a) Reciprocal of price index number.
(b) Equal to price index number.
(c) Unequal to price index number.
(d) None of these.
Purchasing power of money is the reciprocal of price index.
So, Option (a) is correct

19. Consumer price index number goes up from 110 to 200 and the Salary of a worker is also raised from Rs.325 to 500. To maintain previous standard of living, salary should increase:
(a) Rs.85
(b) Rs.90.91
(c) Rs.98.25
(d) None of these
Current salary = $\displaystyle \frac{{Current\text{ }consumer\text{ }price\text{ }index}}{{Previous\text{ }consumer\text{ }price\text{ }index}}\times Previous\text{ }salary$
$\displaystyle =\frac{{200}}{{110}}\times 325=590.91$
$\displaystyle \therefore$ Addition salary
= 590.91 – 500 = 90.91
So, Option (a) is correct

Index Number – MCQ

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