ICAR AICE-JRF/SRF (PhD admission and fellowship) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersThe statistics every later subject leans on: describing data, probability, sampling, testing and relating variables, plus the mathematics economists use.
In the exams: agricultural master's entrance examinations, elements of statistics and tests of significance (heavy); agricultural master's entrance examinations, agribusiness quantitative units (present); quantitative sections of agricultural development bank officer recruitment and agricultural field officer recruitment in banking
ICAR AICE-JRF/SRF (PhD) and ASRB NET (Agricultural Economics / Agri-Business Management)
Statistics as the base of research methods, econometrics and production economics: sampling distributions and estimator properties, ANOVA, partial correlation, regression coefficient properties, Fisher's index and its tests, compound growth rates, and calculus-based optimisation (MPP = price ratio, Lagrange multipliers, Cobb-Douglas elasticities).
How our questions for ICAR AICE-JRF/SRF spread across the units of Business Statistics & Quantitative Methods. Difficulty: 7 easy, 32 medium, 24 hard.
| Tests of significance | 8 | |
| Mathematics for economics: linear algebra and integration | 8 | |
| Index numbers | 7 | |
| Mathematics for economics: differentiation and optimisation | 7 | |
| Sampling techniques | 6 | |
| Regression | 5 | |
| Time series | 5 | |
| Probability distributions | 4 | |
| Correlation | 4 | |
| Measures of central tendency | 3 | |
| Measures of dispersion | 3 | |
| Probability | 3 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Monthly fertiliser purchases (kg) of 50 farmers are grouped as: 0-10: 5 farmers, 10-20: 12, 20-30: 20, 30-40: 8, 40-50: 5. Using the grouped-data formula, what is the modal purchase?
C. 24.0 kg
Modal class 20-30 (f1 = 20), f0 = 12, f2 = 8. Mode = L + ((f1 - f0)/(2f1 - f0 - f2)) x h = 20 + (8/20) x 10 = 24.0 kg. 25.0 is the class mid-point; 26.0 swaps f0 and f2 (numerator f1 - f2 = 12); 26.7 uses only (f1 - f2) = 12 as the denominator.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
Which statement about averages is correct?
A. The sum of absolute deviations is least when taken about the median
Absolute deviations are minimised about the median; squared deviations are minimised about the mean, and it is deviations from the mean (not the median) that sum to zero. For positive values AM >= GM >= HM, so the GM is never greater than the AM.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
Landholdings in a district have Q1 = 1.2 ha, median 2.0 ha and Q3 = 3.6 ha. What is Bowley's coefficient of skewness?
B. 0.33
Bowley's Sk = (Q3 + Q1 - 2 Md)/(Q3 - Q1) = (3.6 + 1.2 - 4.0)/(2.4) = 0.8/2.4 = 0.33, positive skew (the upper quartile lies further from the median). 0.80 forgets to divide; -0.33 reverses the sign. 0.67 is (Q3 - Md)/(Q3 - Q1), the upper gap alone.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
Next month's mandi price of a pulse (rupees per kg) is forecast as 18 with probability 0.2, 20 with probability 0.5 and 24 with probability 0.3. What are the expected price and its variance?
D. Mean 20.8, variance 4.96
E(X) = 18(0.2) + 20(0.5) + 24(0.3) = 3.6 + 10 + 7.2 = 20.8. E(X^2) = 324(0.2) + 400(0.5) + 576(0.3) = 437.6. Var = E(X^2) - [E(X)]^2 = 437.6 - 432.64 = 4.96. The SD is 2.23; 20.7 is the unweighted mean of the three prices; E(X^2) alone is not the variance.
Further reading: Anderson, Sweeney and Williams, Statistics for Business and Economics
Three fertiliser schedules are each tried on 4 plots. The treatment sum of squares is 60 and the error sum of squares is 90. What is the ANOVA F and the conclusion at 5 per cent (critical F with (2, 9) df = 4.26)?
D. F = 3.00; schedules do not differ significantly
Treatment df = 3 - 1 = 2; error df = 12 - 3 = 9. MS treatment = 60/2 = 30; MS error = 90/9 = 10; F = 3.00 < 4.26. 0.67 is SS treatment/SS error without dividing by df; 2.67 uses error df 8 instead of 9 (30/(90/8)).
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
If each rainfall value is converted from mm to cm and each yield value from q/ha to t/ha, and 10 is then added to every yield value, what happens to the correlation between rainfall and yield?
D. Unchanged
r is independent of change of origin and of scale (for positive scale factors). Only a negative scale factor on one variable flips its sign.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
Which index number formula satisfies both the time reversal test and the factor reversal test?
D. Fisher's ideal index
Fisher's index satisfies time and factor reversal (but not the circular test). Laspeyres and Paasche satisfy neither reversal test.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
When consumers shift purchases toward goods whose prices have risen less, a Laspeyres consumer price index tends to:
A. Overstate the rise in the cost of living
Laspeyres keeps base-period quantities, so it gives too much weight to goods that became relatively dearer and that people bought less of: an upward (substitution) bias. Paasche, with current quantities, tends to the opposite.
Further reading: Anderson, Sweeney and Williams, Statistics for Business and Economics
Link relatives (current year as a percentage of the previous year) of the price of a spice are 110, 105 and 98 for three successive years after the base year. What is the chain index for the third year (base year = 100)?
B. 113.2
Chain index = product of link relatives: 1.10 x 1.05 x 0.98 x 100 = 113.2. 104.3 is the average link relative; 113.0 adds the percentage changes (10 + 5 - 2); 313 adds the relatives.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
Quarterly seasonal indices of fertiliser sales are computed as 130, 90 and 110 for the first three quarters. Under the usual convention, what is the fourth-quarter index?
A. 70
Quarterly indices sum to 400 (average 100). 400 - (130 + 90 + 110) = 70. 100 would be the average, not the missing value. -30 is the deviation from 100 (100 - 130), not the index itself.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
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