"Business Statistics and Research Methods" — Practice

Question 1

The mean of the following 5 daily sales figures (₹'000): 12, 15, 18, 20, 25 is:
(a) 16  (b) 17  (c) 18  (d) 20

Accepted Answer

Mean = (12 + 15 + 18 + 20 + 25) ÷ 5 = 90 ÷ 5 = 18.

Answer: (c) 18. Trap (a) and trap (b) both understate the true sum-based average. Trap (d) mistakes the highest single value in the set for the mean of the whole set.

Question 2

The median of the data set 8, 12, 15, 20, 22, 30 is:
(a) 15  (b) 20  (c) 18  (d) 17.5

Accepted Answer

With 6 (even) observations, the median is the average of the 3rd and 4th values: (15 + 20) ÷ 2 = 17.5.

Answer: (d) 17.5. Trap (a) and trap (b) each pick only one of the two correct middle values instead of averaging them. Trap (c) is a plausible-looking figure that does not match the actual pair of middle values.

Question 3

The mode of the data set 4, 6, 6, 6, 8, 10, 10 is:
(a) 6  (b) 8  (c) 10  (d) There is no mode

Accepted Answer

The value 6 occurs three times, more often than any other value in the set.

Answer: (a) 6. Trap (b) occurs only once. Trap (c) occurs twice, fewer times than 6. Trap (d) is incorrect since a clear single most-frequent value exists in this data set.

Question 4

For the data set 4, 6, 8, 10, 12 (treated as the entire population), the variance is:
(a) 2.83  (b) 8  (c) 6  (d) 10

Accepted Answer

Mean = 40 ÷ 5 = 8. Deviations: −4, −2, 0, 2, 4; squared: 16, 4, 0, 4, 16; sum = 40. Variance = 40 ÷ 5 = 8.

Answer: (b) 8. Trap (a) is actually the standard deviation (√8 ≈ 2.83), not the variance — a very common mix-up. Trap (c) and trap (d) are both plausible nearby numbers that don't match the actual sum of squared deviations divided by 5.

Question 5

Standard deviation is most precisely defined as:
(a) The difference between the highest and lowest values in a data set  (b) The mean of the absolute deviations from the mean  (c) The positive square root of the variance  (d) The middle value of a ranked data set

Accepted Answer

Standard deviation is defined, by construction, as the positive square root of the variance, bringing the measure back into the original units of the data.

Answer: (c). Trap (a) defines range, a cruder and different measure of dispersion. Trap (b) defines mean absolute deviation, a related but distinct measure. Trap (d) defines the median, a measure of central tendency, not dispersion.

Question 6

A data set has mean 8 and standard deviation 2.83. Its coefficient of variation is closest to:
(a) 8%  (b) 28.3%  (c) 50%  (d) 35.4%

Accepted Answer

CV = (Standard Deviation ÷ Mean) × 100 = (2.83 ÷ 8) × 100 ≈ 35.4%.

Answer: (d) 35.4%. Trap (a) mistakes the mean itself for a percentage figure. Trap (b) miscalculates by inverting which figure is divided by which. Trap (c) is a plausible round number but does not match the actual computed ratio.

Question 7

For the paired data X: 2, 4, 6, 8 and Y: 3, 7, 5, 9, Karl Pearson's coefficient of correlation is:
(a) 0.8  (b) 0.5  (c) 1.0  (d) 0.3

Accepted Answer

ΣX=20, ΣY=24, ΣXY=136, ΣX²=120, ΣY²=164, n=4. Numerator = (4×136) − (20×24) = 64. Both brackets under the root work out to 80, so the denominator = √(80×80) = 80. r = 64 ÷ 80 = 0.8.

Answer: (a) 0.8. Trap (b) and trap (d) both understate the strength of the actual linear association in this data. Trap (c) would imply a perfect correlation, which the scatter in this data does not show.

Question 8

For the same paired data (X: 2, 4, 6, 8; Y: 3, 7, 5, 9), the regression equation of Y on X is:
(a) Y = 0.8 + 2X  (b) Y = 2 + 0.8X  (c) Y = 8 + 0.64X  (d) Y = 2 − 0.8X

Accepted Answer

b = [n·ΣXY − ΣX·ΣY] ÷ [n·ΣX² − (ΣX)²] = 64 ÷ 80 = 0.8. a = (ΣY − b·ΣX) ÷ n = (24 − 0.8×20) ÷ 4 = 8 ÷ 4 = 2. Regression line: Y = 2 + 0.8X.

Answer: (b) Y = 2 + 0.8X. Trap (a) swaps the intercept and slope values. Trap (c) invents figures that don't follow from this data's actual sums. Trap (d) reverses the sign of the slope, implying a negative relationship where the data shows a positive one.

Question 9

A quality inspector selects every 10th item coming off a production line for inspection, starting from a randomly chosen item among the first 10. This is an example of:
(a) Stratified sampling  (b) Cluster sampling  (c) Systematic sampling  (d) Convenience sampling

Accepted Answer

Selecting units at a fixed interval after a random starting point is the defining feature of systematic sampling.

Answer: (c) Systematic sampling. Trap (a) would require dividing the population into distinct strata first, which isn't described here. Trap (b) would require selecting entire natural groups, not individual items at a fixed interval. Trap (d) describes sampling based purely on ease of access, not a fixed, rule-based interval.

Question 10

A researcher divides a company's employees into three strata — junior, middle, and senior management — and draws a proportionate random sample from each stratum separately. This is an example of:
(a) Cluster sampling  (b) Systematic sampling  (c) Convenience sampling  (d) Stratified sampling

Accepted Answer

Dividing the population into homogeneous groups and sampling proportionately from within each group is the defining feature of stratified sampling.

Answer: (d) Stratified sampling. Trap (a) would instead select only some management levels wholesale rather than sampling within all of them. Trap (b) would require a fixed selection interval rather than proportionate strata-wise sampling. Trap (c) describes selecting whoever is easiest to reach, with no structured division at all.

Question 11

In the classic courtroom analogy for hypothesis testing, where the null hypothesis is 'the defendant is innocent,' convicting an innocent person corresponds to:
(a) Type I error  (b) Type II error  (c) A correctly accepted null hypothesis  (d) A correctly rejected alternative hypothesis

Accepted Answer

Convicting an innocent defendant means rejecting a null hypothesis ('innocent') that is actually true — precisely the definition of a Type I error.

Answer: (a) Type I error. Trap (b) would instead correspond to acquitting a genuinely guilty defendant (failing to reject a false null hypothesis). Trap (c) and trap (d) both describe outcomes where the decision matches the underlying truth, which a wrongful conviction does not.

Question 12

The null hypothesis (H0) in a statistical significance test is best described as:
(a) The hypothesis the researcher hopes to prove  (b) A statement of no difference or no effect, tested for possible rejection  (c) The hypothesis automatically accepted if the sample size is large  (d) A hypothesis that can never be rejected regardless of the evidence

Accepted Answer

H0 always states the status quo — no difference or no effect — and is precisely what the test evaluates for possible rejection in favour of the alternative.

Answer: (b). Trap (a) describes the alternative hypothesis (H1), which researchers typically hope the evidence supports. Trap (c) invents a sample-size rule with no basis in hypothesis-testing theory. Trap (d) is wrong on its face — H0 is explicitly a hypothesis that CAN be rejected given sufficient evidence.

Question 13

Which of the following correctly orders the first three steps of the business research process?
(a) Research design, Problem formulation, Literature review  (b) Literature review, Research design, Problem formulation  (c) Problem formulation, Literature review, Research design  (d) Data collection, Problem formulation, Research design

Accepted Answer

The process must begin with formulating the research problem, since the literature review and research design both depend on knowing exactly what question is being investigated.

Answer: (c). Trap (a) and trap (b) both place problem formulation out of its required first position. Trap (d) begins with data collection, which cannot meaningfully happen before the problem has even been formulated.

Question 14

A card is drawn at random from a well-shuffled deck of 52 playing cards. The probability that it is either a king or a spade is:
(a) 4/52  (b) 17/52  (c) 13/52  (d) 16/52

Accepted Answer

By the addition theorem: P(King or Spade) = P(King) + P(Spade) − P(King of Spades) = 4/52 + 13/52 − 1/52 = 16/52 (= 4/13).

Answer: (d) 16/52. Trap (a) and trap (c) each give only one of the two individual probabilities without combining them. Trap (b) adds the two probabilities without subtracting the overlap, double-counting the king of spades.

Practice — "Business Statistics and Research Methods"

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