SSC CGL Statistics – Index Numbers – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Index Numbers – Level 2 · Exam Level · Paper II Sprint – 15 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Σp₀q₀ = 200, Σp₁q₀ = 250, Σp₀q₁ = 250, Σp₁q₁ = 288. Laspeyres' price index is:

Correct Answer: D [125]

Explanation:

Answer: 125. 250/200 × 100 = 125.

2.  
With the same data (Σp₀q₀ = 200, Σp₁q₀ = 250, Σp₀q₁ = 250, Σp₁q₁ = 288), Paasche's price index is:

Correct Answer: C [115.2]

Explanation:

Answer: 115.2. 288/250 × 100 = 115.2.

3.  
With the same data, Fisher's ideal price index is:

Correct Answer: B [120]

Explanation:

√(125 × 115.2) = √14,400 = 120.

4.  
With the same data, the Marshall–Edgeworth price index (to two decimals) is:

Correct Answer: A [119.56]

Explanation:

(Σp₁q₀ + Σp₁q₁)/(Σp₀q₀ + Σp₀q₁) × 100 = 538/450 × 100 ≈ 119.56.

5.  
Two-quantity comparisonWith the same data:
Quantity I: Fisher's index
Quantity II: Dorbish–Bowley index

Correct Answer: B [Quantity I < Quantity II]

Explanation:

Fisher = GM = 120; Dorbish–Bowley = AM = (125 + 115.2)/2 = 120.1.

6.  
Assertion–Reason
A: Fisher's index is called the ideal index.
R: It satisfies both the time reversal and the factor reversal tests.

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

Passing both reversal tests (and the unit test) is why it is called ideal.

7.  
Index numbers on base 2015: 2019 – 120, 2022 – 150, 2024 – 180. Shifted to base 2022, the index for 2024 is:

Correct Answer: D [120]

Explanation:

Answer: 120. 180 ÷ 150 × 100 = 120.

8.  
An old series (base 2010) stands at 160 in 2020. A new series with base 2020 = 100 gives 115 for 2023. Spliced to the old base, the 2023 index is:

Correct Answer: C [184]

Explanation:

Answer: 184. 115 × 160/100 = 184.

9.  
A salary rose from ₹ 30,000 (CPI 120) to ₹ 45,000 (CPI 160). The real salary in the later year, at base-period prices (CPI = 100), is:

Correct Answer: C [₹ 28,125]

Explanation:

45,000 × 100/160 = 28,125 (the earlier one is 25,000, so a real rise of 12.5%).

10.  
Diagram-basedGroup indices and weights (w) of a consumer price index are shown.

The overall index is:

Correct Answer: A [132.5]

Explanation:

Σwi/Σw = (6,000 + 2,400 + 2,100 + 2,750)/100 = 132.5.

11.  
Link relatives for three successive years are 110, 120 and 90 (first year's base = 100). The chain index for the third year is:

Correct Answer: B [118.8]

Explanation:

1.10 × 1.20 × 0.90 × 100 = 118.8.

12.  
Trick SpotterLaspeyres and Paasche indices are known. The quickest way to get Fisher's index is:

Correct Answer: D [Take √(L × P)]

Explanation:

Fisher is defined as the geometric mean of L and P.

13.  
Spot My Mistake“Laspeyres' index = Σp₁q₁ ÷ Σp₀q₁ × 100.” The formula written is actually:

Correct Answer: A [Paasche's index]

Explanation:

Current-year quantities as weights = Paasche.

14.  
When the consumer price index is 125 (base 100), the purchasing power of a rupee (in base-period rupees) is:

Correct Answer: B [₹ 0.80]

Explanation:

Answer: ₹ 0.80. 100 ÷ 125 = 0.80.

15.  
A weighted harmonic mean of price relatives, using current-year values p₁q₁ as weights, is identical to:

Correct Answer: C [Paasche's price index]

Explanation:

Σp₁q₁ ÷ Σ[p₁q₁/(p₁/p₀)] = Σp₁q₁/Σp₀q₁ – exactly Paasche.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics

📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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