ICAR AIEEA-PG (Master's admission and PG scholarship) · 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 AIEEA-PG Group 06 Social Sciences (Agricultural Economics; Agricultural Extension)
Elements of statistics and tests of significance: mean, median, mode, SD and CV computations; probability rules; binomial, Poisson and normal; SRS and stratified sampling; z, t, chi-square and F tests with stated critical values; correlation and regression coefficients; index number formulas and tests; time-series components and trend.
ICAR AIEEA-PG Group 19 Agri-Business Management (Units V and VII)
Quantitative ability and data interpretation: averages, percentages, growth rates, weighted means, probability and quick calculations from tables.
How our questions for ICAR AIEEA-PG spread across the units of Business Statistics & Quantitative Methods. Difficulty: 27 easy, 41 medium, 17 hard.
| Tests of significance | 12 | |
| Probability distributions | 8 | |
| Sampling techniques | 8 | |
| Regression | 8 | |
| Time series | 8 | |
| Correlation | 7 | |
| Index numbers | 7 | |
| Measures of central tendency | 6 | |
| Measures of dispersion | 6 | |
| Mathematics for economics: differentiation and optimisation | 6 | |
| Mathematics for economics: linear algebra and integration | 5 | |
| Probability | 4 |
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
Landholdings in a district have first quartile 1.2 ha and third quartile 3.6 ha. What is the quartile deviation?
A. 1.2 ha
Quartile deviation = (Q3 - Q1)/2 = (3.6 - 1.2)/2 = 1.2 ha. 2.4 ha is the interquartile range, not half of it; 0.5 is the coefficient of QD, (Q3 - Q1)/(Q3 + Q1) = 2.4/4.8, a unit-free number.
Further reading: Gupta and Kapoor, Fundamentals of Mathematical Statistics
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
A regression of yield (q/ha) on rainfall (mm) fitted over rainfall of 600 to 1,000 mm is Yield = 2.2 + 0.026 Rainfall. A field that received 850 mm yielded 25.0 q/ha. What is its residual?
A. +0.7 q/ha
Predicted = 2.2 + 0.026 x 850 = 24.3; residual = actual - predicted = 25.0 - 24.3 = +0.7. Predicted minus actual has the wrong sign; 24.3 is the prediction itself. +2.9 drops the intercept from the prediction (25.0 - 22.1).
Further reading: OpenStax, Introductory Business 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
A wholesale price index stands at 150 in the current year and at 125 in the year chosen as the new base. What is the current value on the new base?
C. 120
New index = old index/old index of new base year x 100 = 150/125 x 100 = 120. 187.5 multiplies instead of divides; 25 is the difference in points.
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
The trend value of a processor's sales for next quarter is 900 tonnes and that quarter's seasonal index is 85. Using the multiplicative model, what is the forecast?
D. 765 tonnes
Forecast = trend x seasonal index/100 = 900 x 0.85 = 765. 1,059 divides by 0.85 (that deseasonalises, it does not forecast); 815 subtracts 85 as if the model were additive. 985 adds 85 instead.
Further reading: Anderson, Sweeney and Williams, Statistics for Business and Economics
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