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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 331
In a frequency distribution with class intervals 0-10, 10-20, 20-30 and so on, the class mark of the interval 20-30 is:
Select an option first.
Correct answer: B — 25
Explanation: The class mark, or mid-value, is the average of the lower and upper limits: (20 + 30)/2 = 25. It is the value used to represent the whole class when computing the mean or standard deviation of grouped data, on the assumption that the observations are evenly spread within the class - which is the source of grouping error.
Question 332
The classical or mathematical definition of probability assumes that the outcomes are:
Select an option first.
Correct answer: B — Equally likely, mutually exclusive and exhaustive
Explanation: The classical definition takes favourable cases over total cases, which is meaningful only if every outcome is equally likely and the list is complete and non-overlapping. Where that cannot be assumed, the EMPIRICAL definition based on long-run relative frequency is used instead - distractor C describes that.
Question 333
The coefficient of determination measures:
Select an option first.
Correct answer: C — The proportion of the variation in the dependent variable explained by the independent variable
Explanation: Being r squared, it always lies between 0 and 1 and is read as a percentage of variation explained. The remainder, 1 minus r squared, is the coefficient of NON-determination. Unlike r itself it carries no sign, so it says nothing about the direction of the relationship - only the strength.
Question 334
If the coefficient of correlation is -0.9, the coefficient of determination is:
Select an option first.
Correct answer: D — 0.81
Explanation: The coefficient of determination is r squared = 0.81, and squaring destroys the sign, so it is positive whatever the direction of the relationship. It cannot be negative, which disposes of two options at once. Here 81% of the variation in the dependent variable is explained, despite the relationship being inverse.
Question 335
The coefficient of quartile deviation is given by:
Select an option first.
Correct answer: D — (Q3 - Q1) divided by (Q3 + Q1)
Explanation: The COEFFICIENT is a relative measure, obtained by dividing the quartile deviation by the average of the two quartiles, which reduces to (Q3 - Q1)/(Q3 + Q1). Distractor A is the quartile deviation itself, an absolute measure in the units of the data. Relative measures are what allow two different distributions to be compared.
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Question 336
A distribution has a mean of 40 and a standard deviation of 8. Its coefficient of variation is:
Select an option first.
Correct answer: B — 20%
Explanation: Coefficient of variation = (standard deviation / mean) x 100 = (8/40) x 100 = 20%. Being a pure number it allows the variability of two series measured in different units, or with very different means, to be compared - which a bare standard deviation cannot do. The series with the LOWER coefficient is the more consistent.
Question 337
If every value in a series is increased by 10 PER CENT, the coefficient of variation:
Select an option first.
Correct answer: C — Remains unchanged
Explanation: Multiplying every value by 1.1 multiplies both the mean and the standard deviation by 1.1, so their ratio is unaltered. Adding a fixed AMOUNT would be different: the mean would rise while the standard deviation stayed put, lowering the coefficient. Proportional and absolute changes behave quite differently.
Question 338
If the two lines of regression coincide, the coefficient of correlation is:
Select an option first.
Correct answer: B — Plus or minus 1
Explanation: The two regression lines always cross at the point of means, and the angle between them narrows as the correlation strengthens. They coincide only when the relationship is perfect, that is r = +1 or -1, and they are at right angles when r = 0. The angle between them is thus a geometric measure of correlation.
Question 339
Group A has 40 items with a mean of 15 and Group B has 60 items with a mean of 25. The mean of the combined group is:
Select an option first.
Correct answer: C — 21
Explanation: Combined mean = (40 x 15 + 60 x 25) / 100 = (600 + 1,500) / 100 = 21. Distractor A is the simple average of the two means, which would only be right if the groups were equal in size. Because the larger group has the higher mean, the answer must lie above 20 - a check worth making before computing.
Question 340
To compute the combined standard deviation of two groups, one needs:
Select an option first.
Correct answer: A — The means, the standard deviations and the sizes of both groups
Explanation: The combined variance has two parts: a weighted average of the within-group variances, and a term for the deviation of each group mean from the combined mean. Both parts need the sizes as weights, so all three quantities are required. This is why the standard deviations alone can never be simply averaged.
Question 341
The coefficient of variation of series A is 25% and of series B is 15%. It follows that:
Select an option first.
Correct answer: C — B is more consistent
Explanation: The LOWER coefficient of variation indicates the smaller relative dispersion and therefore the greater consistency or uniformity, so B is more consistent. The coefficient is a pure number, which is exactly why the comparison is possible without knowing the means or the units - distractor D misses that point.
Question 342
Two distributions have the same mean but different standard deviations. The one with the higher standard deviation is:
Select an option first.
Correct answer: B — Less consistent
Explanation: A larger standard deviation means the values are more widely scattered about the same central point, so that distribution is less uniform and therefore less consistent. Because the means are equal, the standard deviations may be compared directly - if the means differed, the coefficient of variation would be needed instead.
Question 343
If P(A) = 0.3, then the probability that A does not occur is:
Select an option first.
Correct answer: D — 0.7
Explanation: Either A occurs or it does not, and the two possibilities are exhaustive and mutually exclusive, so their probabilities sum to 1. Hence P(not A) = 1 - 0.3 = 0.7. Computing the complement is often far easier than the event itself - 'at least one' problems are almost always solved as 1 minus the probability of none.
Question 344
The components of a time series are:
Select an option first.
Correct answer: A — Secular trend, seasonal variation, cyclical variation and irregular variation
Explanation: A time series is analysed into a long-term secular TREND, regular within-year SEASONAL movements, longer business-cycle CYCLICAL swings, and unpredictable IRREGULAR or random variation. Separating them is what allows a seasonally adjusted figure to be computed and a trend to be projected.
Question 345
If Laspeyres' index is 110 and Paasche's index is 108, Fisher's ideal index is approximately:
Select an option first.
Correct answer: C — 109.0
Explanation: Fisher's index is the geometric mean of the two: the square root of (110 x 108) = the square root of 11,880 = 108.995, or about 109. Distractor B is the ARITHMETIC mean, which is always slightly the larger; the geometric mean must lie between the two indices and below their arithmetic mean.
Question 346
If the coefficient of correlation is 0.6, the coefficient of determination is:
Select an option first.
Correct answer: A — 36%
Explanation: The coefficient of determination is r squared = 0.36, that is 36% of the variation in the dependent variable explained by the independent one. Note how much smaller this is than the correlation itself - a moderate-looking r of 0.6 accounts for barely a third of the variation, which is the point worth making in a written answer.
Question 347
If r = 0.8 for a sample of 25 pairs, the probable error of the coefficient of correlation is approximately:
Select an option first.
Correct answer: B — 0.0486
Explanation: Probable error = 0.6745 x (1 - r squared) divided by the square root of n = 0.6745 x 0.36 / 5 = 0.0486. Since r of 0.8 far exceeds six times this probable error, the correlation is highly significant - and stating that conclusion is what earns the second mark.
Question 348
Given P(A) = 0.6, P(B) = 0.4 and P(A and B) = 0.24, the value of P(A given B) is:
Select an option first.
Correct answer: B — 0.6
Explanation: P(A given B) = P(A and B) / P(B) = 0.24 / 0.4 = 0.6. Notice that this equals P(A) itself, which tells us the events are INDEPENDENT - knowing that B has occurred does not change the chance of A. Testing whether the joint probability equals the product of the marginals is the standard check for independence.
Question 349
In a binomial distribution the number of trials must be:
Select an option first.
Correct answer: A — Finite and fixed in advance
Explanation: The binomial requires a fixed finite number of independent trials, each with only two outcomes and a constant probability of success. If n is large and p small with np constant, the distribution tends to the Poisson, which is defined for an unlimited number of occurrences - which is why n must be stated for a binomial but not for a Poisson.
Question 350
The relation Mode = 3 Median - 2 Mean may be applied:
Select an option first.
Correct answer: A — To a moderately skewed distribution, as an approximation
Explanation: The relation is empirical rather than exact, derived from observation of moderately skewed distributions, so it gives an approximation and not a precise value. In a perfectly symmetrical distribution all three averages coincide and the relation holds trivially; in a heavily skewed one it can mislead.
Question 351
If money wages rise by 20% while the cost of living index rises by 25%, real wages have:
Select an option first.
Correct answer: C — Fallen
Explanation: Real wages equal money wages divided by the price index. Since prices have risen faster than wages, the same money buys less and real wages have fallen - by about 4%, since 120/125 is 0.96. Compare the two RATES of change rather than the absolute figures.
Question 352
In a normal distribution, the probability that the variable takes one exact specified value is:
Select an option first.
Correct answer: C — Zero, the distribution being continuous
Explanation: For a continuous distribution probability is represented by AREA, and the area over a single point has zero width and therefore zero size. Probabilities are meaningful only over an interval, which is why normal-distribution questions always ask for the chance of falling between two values or beyond one.
Question 353
The mean of 12 observations was found to be 20. It was later discovered that one observation had been recorded as 53 instead of 35. The corrected mean is:
Select an option first.
Correct answer: C — 18.5
Explanation: The incorrect total is 12 x 20 = 240. Replacing 53 by 35 reduces it by 18 to 222, so the corrected mean is 222/12 = 18.5. Because the recorded figure was too HIGH, the corrected mean must fall below 20 - a direction check that eliminates two options immediately.
Question 354
If the two regression coefficients are 0.8 and 0.5, the coefficient of correlation is:
Select an option first.
Correct answer: C — 0.632
Explanation: The correlation coefficient is the geometric mean of the two regression coefficients: the square root of (0.8 x 0.5) = the square root of 0.40 = 0.632. Its sign is the same as that of the regression coefficients, which are both positive here. Note also that both regression coefficients must always carry the SAME sign, and their product can never exceed 1.
Question 355
If the regression coefficient of x on y is 0.4 and that of y on x is 0.9, the coefficient of correlation is:
Select an option first.
Correct answer: A — 0.60
Explanation: The correlation is the geometric mean of the two regression coefficients: the square root of (0.4 x 0.9) = the square root of 0.36 = 0.60, positive because both coefficients are positive. Distractor B is the product itself, which is the coefficient of DETERMINATION rather than the correlation.
Question 356
A cost of living index measures:
Select an option first.
Correct answer: A — The change in the cost of a fixed basket of goods consumed by a particular class of people
Explanation: The index is constructed for a defined class - industrial workers, for instance - by pricing a fixed basket derived from a family budget enquiry, and it is used for dearness allowance and real wage calculations. Real wage equals money wage divided by the index, multiplied by 100 - the standard follow-up computation.
Question 357
The number of observations falling below the upper limit of a class is given by its:
Select an option first.
Correct answer: D — Less-than cumulative frequency
Explanation: A less-than cumulative frequency accumulates all frequencies up to and including the class concerned. Plotting these against the upper class limits gives the less-than ogive, and the point where it meets the more-than ogive locates the MEDIAN graphically - which is the main reason the two are drawn together.
Question 358
The point at which the less-than and more-than ogives intersect gives the:
Select an option first.
Correct answer: B — Median
Explanation: At the crossing point, the number of observations below the value equals the number above it - which is the definition of the median. Dropping a perpendicular from that intersection to the horizontal axis reads it off directly, and this is the standard graphical method examined for the median.
Question 359
A STATISTIC is:
Select an option first.
Correct answer: A — A characteristic computed from the sample
Explanation: A statistic is computed from sample data and varies from sample to sample - that variation is the sampling distribution. The population equivalent is the PARAMETER. Because a statistic is used to estimate a parameter, the two terms are constantly paired and just as constantly confused.
Question 360
The standard deviation is the square root of:
Select an option first.
Correct answer: D — The arithmetic mean of the squared deviations from the mean
Explanation: Standard deviation is the positive square root of the variance, which is the mean of the squared deviations from the arithmetic mean. Squaring serves two purposes: it removes the signs, and it gives greater weight to larger deviations. Distractor A would always be zero, since deviations from the mean necessarily sum to zero.
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