In a detailed study of annual crow births in India, it was found that there was relatively no
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another
unrelated study, it was found that the revenue from cracker sales in India which remained
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006.
The solid line in the graph below refers to annual sale of crackers and the dashed line refers
to the annual crow births in India. Choose the most appropriate inference from the above
data.
Options:
(A) There is a strong correlation between crow birth and cracker sales.
(B) Cracker usage increases crow birth rate.
(C) If cracker sale declines, crow birth will decline.
(D) Increased birth rate of crows will cause an increase in the sale of crackers.
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.10)**
**1. Governing Concept & Question Classification**:
- **Section**: General Aptitude (GA)
- **Question Type**: **MCQ** (2 Marks)
- **Topic**: Data Interpretation & Critical Reasoning (Correlation vs. Causation)
**2. Detailed Step-by-Step Analysis**:
- The problem presents two independent, unrelated studies:
1. Annual crow births in India showed no growth during 2002–2004 and a sudden spike from 2004 to 2005.
2. Revenue from cracker sales in India remained flat from 2002 to 2004 and also saw a sudden spike in 2005 before declining in 2006.
- The two variables trend together (both flat in 2002–2004, both spike in 2004–2005). Statistically, when two variables exhibit similar patterns over the same time period, they display **correlation**.
- However, as explicitly noted, these were "unrelated studies," and a shared trend does **not** imply a causal relationship (*cum hoc ergo propter hoc* fallacy). Therefore, claiming that cracker sales caused crow births, or vice versa, is an invalid causal leap.
- Thus, the only statistically sound inference is that there is a strong correlation between crow births and cracker sales over this timeframe.
- **Option-by-Option Evaluation**:
- **Option (A) [CORRECT]**: *"There is a strong correlation between crow birth and cracker sales."* This correctly states the observational statistical relationship without improperly asserting causation.
- **Option (B) [INCORRECT]**: Asserts false causation (that cracker usage causes crow births).
- **Option (C) [INCORRECT]**: Extrapolates an unproven causal link into future predictions.
- **Option (D) [INCORRECT]**: Asserts an absurd reverse causal relationship.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).
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