Economics Skill Enhancement Course
Data Analysis and Statistical Methods
Yeh textbook Economics Skill Course ke liye ek complete manual hai. Iss me Primary aur Secondary Data, Probability Sampling, Ogive Curves, Continuous Series me Mean/Median/Mode, Standard Deviation ($\sigma$), Coefficient of Variation (CV), aur Fisher's Ideal Index Time/Factor Reversal Tests ke step-by-step solved numericals pure Hinglish me samjhaye gaye hain.
Fisher's Index
Time & Factor Reversal Proofs
CV Solved Numerical
Consistency Analysis Formulas
Empirical Mode
Mode = 3 Median - 2 Mean
Unit I
Data Collection and Sampling Techniques
1.1
Primary vs. Secondary Data
| Parameter | Primary Data | Secondary Data |
|---|---|---|
| Origin | First-hand data collected by investigator for specific purpose. | Second-hand data compiled from existing publications. |
| Collection Methods | Questionnaires, interviews, direct observation, surveys. | Government reports (NSSO, Census, RBI bulletins), research journals. |
| Cost & Time | High cost, labor intensive, time consuming. | Cost effective and immediately accessible. |
1.2
Sampling Methods: Probability vs. Non-Probability
Probability Sampling Methods:
- Simple Random Sampling: Every population item has an equal, non-zero selection chance (Lottery method, Random number table).
- Stratified Random Sampling: Population divided into non-overlapping strata; samples drawn proportionally from each stratum.
- Systematic Sampling: Selecting every $k$-th item after a random start ($k = N/n$).
Unit IV
Index Numbers and Statistical Report Writing
4.1
Fisher's Ideal Index & Reversal Tests
Fisher's Ideal Price Index Formula:
$$P_{01}^F = \sqrt{L \times P} = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100$$
Reversal Tests Verification:
1. Time Reversal Test: $P_{01} \times P_{10} = 1$
2. Factor Reversal Test: $P_{01} \times Q_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0} = \text{True Value Ratio}$.
Fisher's index satisfies both tests and is therefore termed the 'Ideal' Index.
Exam Special
Examination Question Bank & Revision Tools
Quick Revision Flashcards
What is Fisher's index formula?
√(Laspeyres × Paasche).
What does Ogive intersection yield?
The Median value.
Formula for Coefficient of Variation (CV)?
CV = (σ / Mean) × 100.
Practice MCQs
Q1. Which index number satisfies both Time Reversal and Factor Reversal Tests?
Explanation: Fisher's index is the geometric mean of Laspeyres and Paasche and satisfies both fundamental reversal tests.
Key Terms Glossary
Coefficient of Variation
Relative measure of dispersion expressing standard deviation as percentage of arithmetic mean.
Ogive
Cumulative frequency curve used to graphically estimate median and quartiles.