NABARD Assistant Manager Grade A (RDBS) · India · National Bank for Agriculture and Rural Development
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
How our questions for NABARD Assistant Manager Grade A spread across the units of Business Statistics & Quantitative Methods. Difficulty: 11 easy, 5 medium, 2 hard.
| Measures of central tendency | 3 | |
| Probability distributions | 3 | |
| Probability | 2 | |
| Sampling techniques | 2 | |
| Index numbers | 2 | |
| Time series | 2 | |
| Measures of dispersion | 1 | |
| Tests of significance | 1 | |
| Correlation | 1 | |
| Regression | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A farmer sells 20 quintals of maize at 2,000 currency units per quintal, 30 quintals at 2,200 and 50 quintals at 2,100. What average price per quintal did the farmer realise?
B. 2,110 currency units
Use the weighted mean with quantities as weights: (20 x 2,000 + 30 x 2,200 + 50 x 2,100) / 100 = (40,000 + 66,000 + 105,000) / 100 = 2,110. The simple mean of the three prices (2,100) ignores that different quantities were sold at each price. 2,098 is the geometric mean of the three prices, which also ignores quantities; 2,070 mismatches lots and prices (20 with 2,200, 30 with 2,100, 50 with 2,000).
Further reading: Anderson, Sweeney and Williams, Statistics for Business and Economics
In a block, 40 marginal farmers have an average income of 30 thousand currency units a month and 60 small farmers have an average of 25 thousand. What is the combined average income of the 100 farmers?
C. 27 thousand rupees
Combined mean = (40 x 30 + 60 x 25)/100 = (1,200 + 1,500)/100 = 27. 27.5 is the unweighted average of the two group means, which ignores that the groups differ in size.
Further reading: OpenStax, Introductory Business Statistics
Two fair dice are rolled in a game at a farmers' fair. What is the probability that the sum is 7?
D. 1/6
Of 36 equally likely outcomes, six give a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). 6/36 = 1/6. 1/11 wrongly treats the 11 possible sums (2 to 12) as equally likely.
Further reading: OpenStax, Introductory Business Statistics
Seed from a lot germinates with probability 0.9, independently. If 5 seeds are sown, what is the probability that exactly 4 germinate?
B. 0.3281
Binomial: P(X = 4) = 5C4 (0.9)^4 (0.1)^1 = 5 x 0.6561 x 0.1 = 0.3281. Omitting the 5C4 = 5 arrangements gives 0.0656; 0.6561 ignores the one failure. 0.8000 is simply 4/5.
Further reading: OpenStax, Introductory Business Statistics
Grain moisture readings at a procurement centre are normally distributed. Approximately what percentage of readings lie within two standard deviations of the mean?
B. 95.4 per cent
For a normal distribution about 68.3, 95.4 and 99.7 per cent of values lie within 1, 2 and 3 SD of the mean. Exactly 95 per cent lie within 1.96 SD.
Further reading: OpenStax, Introductory Business Statistics
A bank expects about 40 per cent of farmers in its area to hold crop insurance and wants to estimate the proportion within plus or minus 5 percentage points at 95 per cent confidence (z = 1.96). What minimum sample size is needed?
B. 369
n = z^2 p(1 - p)/E^2 = 3.8416 x 0.24/0.0025 = 368.79, rounded up to 369. 385 uses p = 0.5, the conservative choice when p is unknown; here a prior estimate is available. 96 omits z^2 (0.24/0.0025); 20 forgets to square (z sqrt(pq)/E = 19.2).
Further reading: Cochran, Sampling Techniques
The correlation between fertiliser dose and yield in a trial is 0.8. What proportion of the variation in yield is associated with fertiliser dose?
B. 64 per cent
The coefficient of determination r^2 = 0.8^2 = 0.64, so 64 per cent. r itself (80 per cent) overstates explained variation; 89 per cent is sqrt(0.8). 36 per cent is 1 - r^2, the unexplained share.
Further reading: OpenStax, Introductory Business Statistics
A regression of monthly milk sales (litres) on number of cows gives Sales = 120 + 250 x Cows. What are the predicted sales for a farm with 6 cows?
C. 1,620 litres
120 + 250 x 6 = 120 + 1,500 = 1,620. 1,500 drops the intercept; 370 adds 250 once. 2,220 multiplies the intercept by 6 as well ((120 + 250) x 6).
Further reading: OpenStax, Introductory Business Statistics
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
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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