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Free CA Quantitative Aptitude Practice Questions & Answers
500 exam-style Quantitative Aptitude questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 301
Which of the following is a RELATIVE measure of dispersion?
Select an option first.
Correct answer: B — Coefficient of variation
Explanation: Relative measures are pure numbers obtained by dividing an absolute measure by an appropriate average, and the coefficient of variation - standard deviation over mean, times 100 - is the leading example. The other three are absolute measures expressed in the units of the data, so they cannot compare distributions measured differently.
Question 302
The arithmetic mean of 25 observations is 40. If 5 is added to each observation, the new mean is:
Select an option first.
Correct answer: D — 45
Explanation: Adding a constant to every value shifts the mean by the same constant, giving 45. The number of observations is irrelevant here - it is offered only to tempt a multiplication. Note that the standard deviation would be entirely unchanged, since the spread has not altered.
Question 303
If P(A) = 1/3 and P(B) = 1/4 and the two events are independent, then P(A or B) is:
Select an option first.
Correct answer: C — 1/2
Explanation: Independence gives P(A and B) = 1/3 x 1/4 = 1/12. The addition rule then gives 1/3 + 1/4 - 1/12 = 4/12 + 3/12 - 1/12 = 6/12 = 1/2. Distractor A omits the subtraction, which would be correct only if the events were mutually exclusive - and independent events with non-zero probabilities never are.
Question 304
The total area under a normal probability curve is:
Select an option first.
Correct answer: D — 1
Explanation: The total area under any probability density curve is 1, representing total certainty, and the normal curve is no exception despite extending infinitely in both directions. Half the area lies on each side of the mean, which is why the probability of exceeding the mean is exactly 0.5.
Question 305
In a normal distribution, the area between the mean and z = 1.96 is approximately:
Select an option first.
Correct answer: B — 0.475
Explanation: The table value from the mean to z = 1.96 is 0.4750. Doubling it gives 0.95, the familiar 95% lying within 1.96 standard deviations of the mean on BOTH sides - which is distractor A. Check whether the question asks for one tail, the area from the mean, or the central band.
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Question 306
The mean of 100 observations was computed as 45. It was later found that one observation had been recorded as 83 instead of 38. The corrected mean is:
Select an option first.
Correct answer: C — 44.55
Explanation: The incorrect total was 100 x 45 = 4,500. Replacing 83 by 38 reduces it by 45 to 4,455, so the corrected mean is 44.55. Because the wrongly recorded figure was too HIGH, the corrected mean must be lower than 45 - a direction check that eliminates two distractors before any arithmetic is done.
Question 307
The arithmetic mean of 5, 8, 12, 15 and 20 is:
Select an option first.
Correct answer: D — 12
Explanation: The total is 60 and there are 5 observations, so the mean is 12. A useful check on any mean: it must lie between the smallest and the largest observation, here between 5 and 20, and for a roughly even spread it will sit near the middle of that range.
Question 308
The arithmetic mean of 3, 7, 7, 9 and 14 is:
Select an option first.
Correct answer: A — 8
Explanation: The total is 40 and there are 5 observations, so the mean is 8. Every observation counts, including the repeat - the 7 appears twice and must be added twice. Distractor B is the mode and the median, both of which happen to be 7 here, which is why the question distinguishes them.
Question 309
Data arranged in ascending or descending order of magnitude is called:
Select an option first.
Correct answer: A — An array
Explanation: Arranging raw data in order produces an array, which is the first step towards finding the range, the median or the quartiles. Grouping the array into classes then produces a frequency distribution. Ordering is what turns unusable raw data into something a positional measure can be read from.
Question 310
Three fair coins are tossed. The probability of getting AT LEAST one head is:
Select an option first.
Correct answer: D — 7/8
Explanation: It is far quicker to compute the complement: the only outcome with no head is TTT, with probability 1/8, so the answer is 1 - 1/8 = 7/8. Whenever a question says 'at least one', reach for the complement first - listing the favourable cases directly takes several times as long.
Question 311
The most suitable average for computing an average rate of growth is the:
Select an option first.
Correct answer: D — Geometric mean
Explanation: Growth compounds multiplicatively, so the correct average of successive growth factors is their geometric mean; the arithmetic mean would overstate the true average rate. The same reasoning makes the geometric mean appropriate for averaging ratios, index numbers and price relatives.
Question 312
Which of the following averages CANNOT be determined graphically?
Select an option first.
Correct answer: B — Arithmetic mean
Explanation: The median and quartiles are read off the ogive, and the mode from the histogram by joining the corners of the modal rectangle. The arithmetic mean requires the actual totals and can only be computed, not read from a graph. This distinction between computed and located averages is a recurring theory question.
Question 313
Base shifting of an index number series means:
Select an option first.
Correct answer: B — Recomputing the series so that a different year becomes the base
Explanation: Each index is divided by the index of the new base year and multiplied by 100, converting the whole series to the new base. It is done when the original base has become too remote or was an abnormal year. Distractor C describes SPLICING and distractor D DEFLATING - three related but distinct operations.
Question 314
In index number construction, the year with which comparisons are made is called the:
Select an option first.
Correct answer: B — Base year
Explanation: The base year is the period of comparison, whose index is set at 100; the current or given year is the one being compared with it. A suitable base should be a normal year, free of war, famine or unusual price movements, and should not be too distant from the current year - a standard theory point.
Question 315
The mode of the values 2, 3, 3, 4, 4 and 5 is:
Select an option first.
Correct answer: C — 3 and 4, the distribution being bimodal
Explanation: Both 3 and 4 occur twice, more often than any other value, so the distribution has two modes and is bimodal. There is no rule permitting them to be averaged, which is what distractor D proposes. The possibility of no mode or of several is the chief limitation of this measure.
Question 316
For a binomial distribution with n = 10 and p = 0.4, the mean and the variance are respectively:
Select an option first.
Correct answer: C — 4 and 2.4
Explanation: Mean = np = 10 x 0.4 = 4 and variance = npq = 10 x 0.4 x 0.6 = 2.4. In a binomial distribution the variance is ALWAYS less than the mean, because q is less than 1 - a property that distinguishes it from the Poisson distribution, where mean and variance are equal.
Question 317
For a binomial distribution the mean is 6 and the variance is 4. The value of n is:
Select an option first.
Correct answer: B — 18
Explanation: Since np = 6 and npq = 4, dividing gives q = 4/6 = 2/3, so p = 1/3 and n = 6 / (1/3) = 18. The variance of a binomial is always LESS than its mean, because q is below 1 - so a question stating a variance greater than the mean would describe an impossible binomial distribution.
Question 318
For a binomial distribution with n = 5 and p = 0.5, the probability of exactly 5 successes is:
Select an option first.
Correct answer: C — 1/32
Explanation: P(X = 5) = C(5,5) x (0.5) to the power 5 = 1 x 1/32 = 1/32. This is the probability of every trial succeeding, so no combination factor arises. Distractor B, 5/32, is the probability of exactly 4 successes, where C(5,4) = 5 does apply.
Question 319
For a binomial distribution with n = 4 and p = 0.25, the probability of no success is:
Select an option first.
Correct answer: D — 0.3164
Explanation: P(X = 0) = q to the power n = (0.75) to the power 4 = 0.3164. No combination factor arises, since there is only one way for every trial to fail. Distractor C is p to the power 4, the probability that every trial SUCCEEDS - the mirror-image error.
Question 320
Four fair coins are tossed. The probability of exactly two tails is:
Select an option first.
Correct answer: B — 3/8
Explanation: The number of ways of choosing which two of the four coins show tails is C(4,2) = 6, out of 16 equally likely outcomes, giving 6/16 = 3/8. Distractor A assumes that 'two out of four' must mean a probability of one half - a confusion between the proportion and its probability.
Question 321
Bowley's coefficient of skewness is based on:
Select an option first.
Correct answer: C — The quartiles and the median
Explanation: Bowley's measure uses (Q3 + Q1 - 2 Median) divided by (Q3 - Q1), so it rests entirely on positional values. That makes it usable for open-ended distributions, where Pearson's coefficient - built on the mean and mode - cannot be computed at all. Both coefficients lie between -1 and +1.
Question 322
A census enquiry involves:
Select an option first.
Correct answer: A — Studying every unit of the population
Explanation: A census covers every unit, so there is no sampling error at all, but it is costly and slow and may involve more NON-sampling error through the sheer volume of work. Sampling is preferred where the population is large, where testing is destructive, or where results are needed quickly.
Question 323
Under the chain base method of constructing index numbers, the base is:
Select an option first.
Correct answer: A — The immediately preceding year
Explanation: Each year is compared with the year before it, producing link relatives which are then chained together to give a continuous series. The method copes well with a changing basket of goods, since new items can be introduced at any link - a flexibility the fixed base method lacks.
Question 324
A frequency distribution has a final class of 'Rs.1,00,000 and above'. Which measure of DISPERSION can still be computed?
Select an option first.
Correct answer: A — The quartile deviation
Explanation: Quartile deviation needs only Q1 and Q3, which normally fall in closed classes, so the open end does not matter. The range needs the largest value, and both the standard deviation and mean deviation need every class mark - none of which the open class supplies.
Question 325
Correlation measures the degree of association between two variables, whereas regression:
Select an option first.
Correct answer: D — Provides an equation for estimating one variable from the other
Explanation: Correlation yields a single pure number describing the strength and direction of the association; regression fits a line that allows the value of one variable to be estimated from the other. Neither establishes CAUSATION - a high correlation may reflect coincidence or a third factor influencing both, which is the point examiners test.
Question 326
For qualitative data such as the most preferred brand, the appropriate measure of central tendency is the:
Select an option first.
Correct answer: D — Mode
Explanation: The mode is the only average that can be found for purely qualitative or nominal data, since it requires nothing more than counting frequencies. The mean needs arithmetic on the values, and even the median needs an ordering, which nominal categories do not possess.
Question 327
To estimate the value of x from a known value of y, one should use the regression line of:
Select an option first.
Correct answer: A — x on y
Explanation: The line of x on y minimises deviations measured in the x direction and is therefore the correct one for predicting x. Using the line of y on x and rearranging it algebraically gives a different and biased estimate. The two lines coincide only when the correlation is perfect.
Question 328
The regression line of y on x is used to estimate:
Select an option first.
Correct answer: A — y for a given value of x
Explanation: The line of y on x minimises the squared deviations measured in the y direction, so it is the right line for predicting y from a known x. Predicting x from y requires the other line, of x on y. The two lines are different unless the correlation is perfect, when they coincide - using the wrong one is a standard error.
Question 329
In an inclusive frequency distribution, the class boundaries of the class 20-29 are:
Select an option first.
Correct answer: C — 19.5 and 29.5
Explanation: An inclusive class leaves a gap between 29 and the next lower limit of 30. The boundaries are found by subtracting half the gap from the lower limit and adding it to the upper: 19.5 and 29.5. This correction is essential before computing a median or mode, which assume a continuous scale.
Question 330
The mid-point of a class interval is also known as its:
Select an option first.
Correct answer: B — Class mark
Explanation: The class mark is the average of the lower and upper limits and represents the whole class when computing the mean or standard deviation of grouped data. Class BOUNDARIES are the adjusted limits used to make classes continuous, and class WIDTH is the difference between them - three distinct ideas.
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