SSC Combined Graduate Level - Junior Statistical Officer / Statistical Investigator · India · Staff Selection Commission
Original practice questions written to the published syllabus · not past papersThe first statistics course of every agricultural degree, which is also the statistics unit of AIEEA-PG Group 07: frequency distributions, averages and dispersion, probability and the three named distributions, tests of significance, correlation and regression, and the CRD and RBD. Laisha teaches it to the depth the entrance examines; the Veterinary, Agribusiness and Agricultural Engineering tracks have their own introductory versions.
In the exams: AIEEA-PG Group 07 statistics unit (heavy: the whole unit); AICE-JRF Agronomy Unit 6 and other agricultural subjects' statistics units (present); ASRB NET general statistics (present); SSC CGL JSO statistics paper (heavy)
How our questions for SSC Combined Graduate Level spread across the units of Statistical Methods for Agricultural Sciences. Difficulty: 36 easy, 45 medium, 7 hard.
| Measures of central tendency: arithmetic, geometric and harmonic means, median and mode | 10 | |
| Binomial, Poisson and normal distributions in agricultural data | 9 | |
| Statistics: definition, uses and limitations; frequency distributions and curves | 7 | |
| Correlation and regression and their tests of significance | 7 | |
| Basic principles of experimental design, ANOVA, CRD and RBD | 7 | |
| Measures of dispersion: range, mean deviation, quartile deviation, variance and coefficient of variation | 6 | |
| Probability: addition and multiplication laws, conditional probability and Bayes' theorem | 6 | |
| Random sampling and standard error | 6 | |
| Large-sample (SND) tests for one and two means | 6 | |
| Chi-square tests for goodness of fit and independence of attributes | 6 | |
| Skewness, kurtosis and moments | 5 | |
| Tests of significance: errors, null hypothesis and level of significance | 5 | |
| Student's t-test: one sample, two samples and paired | 4 | |
| F-test for equality of variances | 4 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
The number of tillers per rice hill is an example of which kind of variable?
D. A discrete quantitative variable
Tillers are counted, so the variable takes only whole-number values: discrete. Plant height or grain weight would be continuous; variety name would be a qualitative attribute.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
A frequency table uses inclusive classes 10-19, 20-29, 30-39 for days to flowering recorded as whole days. What are the true class boundaries of the class 20-29?
D. 19.5 to 29.5
With inclusive classes the gap between 19 and 20 is one unit, so half a unit is subtracted from each lower limit and added to each upper limit: 19.5 to 29.5. Using 20 to 30 treats the classes as exclusive, which they are not.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2 for two events on a farm. What is P(A ∪ B)?
B. 0.7
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 0.5 + 0.4 − 0.2 = 0.7. 0.9 forgets to subtract the overlap, which is counted twice.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
For a fixed sample size, the level of significance of a test is lowered from 5% to 1%. What happens to the probability of a Type II error?
B. It increases
With n fixed, a smaller rejection region makes it harder to reject H₀ when it is false, so β rises and power falls. Only a larger sample can lower both errors together.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Two breeds of sheep give mean fleece weights 52 and 50 (hundreds of grams) from samples of 100 each, with SDs 6 and 8. What is Z for the difference of means?
B. 2.00
SE = √(36/100 + 64/100) = √1.00 = 1.00, so Z = 2/1 = 2.00, just above 1.96 and significant at 5% (two-tailed). 1.43 wrongly adds the two SEs (0.6 + 0.8 = 1.4) instead of their squares; 0.20 divides by √(6² + 8²) = 10 without allowing for n.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
In village A, 60 of 200 farmers adopted drip irrigation; in village B, 40 of 200. Using the pooled proportion, what is Z for the difference?
C. 2.31
p₁ = 0.30, p₂ = 0.20, pooled p = 100/400 = 0.25; SE = √(0.25 × 0.75 × (1/200 + 1/200)) = 0.0433; Z = 0.10/SE = 2.31. Unpooled SE (√(0.21/200 + 0.16/200)) gives 2.32.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Which property does the F distribution have?
C. It is positively skewed and takes only non-negative values
F is a ratio of non-negative quantities, so it ranges from 0 to ∞, is positively skewed, and depends on two df parameters (numerator and denominator).
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
A 2 × 2 table on vaccine use and disease has one expected frequency of 3. Which adjustment is standard?
B. Apply Yates' continuity correction, or use Fisher's exact test
Small expected frequencies make the χ² approximation poor. For 2 × 2 tables, Yates' correction (subtract 0.5 from each |O − E|) or Fisher's exact test is used; χ² must never be computed on percentages or inflated counts.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Plant height is converted from centimetres to metres and 1 m is added to every value. What happens to its correlation with yield?
C. It is unchanged
r is independent of changes of origin and scale (with a positive scale factor), so it is unchanged. The regression coefficient of yield on height, by contrast, would change with the scale.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
Which basic principle of experimental design makes a valid estimate of experimental error possible?
C. Replication
Error is the variation among units treated alike, which can be estimated only if treatments are replicated. Randomisation makes that estimate unbiased; local control reduces it.
Further reading: Snedecor and Cochran, Statistical Methods; Gomez and Gomez, Statistical Procedures for Agricultural Research; Panse and Sukhatme, Statistical Methods for Agricultural Workers
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