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Free CA Quantitative Aptitude Practice Questions & Answers
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100% free · No login to startQuestion 391
In the regression equation y = a + bx, the constant a represents:
Select an option first.
Correct answer: A — The value of y when x is zero
Explanation: The intercept is where the line crosses the y axis, that is the value of y at x = 0. The SLOPE b is the change in y per unit change in x, which is distractor B. Note that the intercept often has no sensible real-world meaning if x = 0 lies far outside the observed data.
Question 392
If P(A) = 0.5, P(B) = 0.4 and P(A union B) = 0.7, then P(A intersection B) is:
Select an option first.
Correct answer: D — 0.2
Explanation: Rearranging the addition rule, P(A intersection B) = 0.5 + 0.4 - 0.7 = 0.2. Since this is not zero, the events are not mutually exclusive; and since 0.2 = 0.5 x 0.4, they happen to be independent as well - a second observation worth making in a written answer.
Question 393
The two lines of regression intersect at:
Select an option first.
Correct answer: D — The point of the means of the two variables
Explanation: Both lines pass through the point whose coordinates are the mean of x and the mean of y, so they always meet there. This is why solving the two regression equations simultaneously yields the two means - a standard question type that would be impossible without this property.
Question 394
Kelly's method of constructing an index number uses weights that are:
Select an option first.
Correct answer: A — Fixed quantities, not necessarily of the base or the current year
Explanation: Kelly's aggregative index uses a set of weights held constant over time, often the average quantities of several years, so it is described as the fixed weight aggregative method. Because the weights never change, it satisfies the CIRCULAR test - which neither Laspeyres, Paasche nor Fisher does.
Question 395
Kurtosis measures:
Select an option first.
Correct answer: D — The peakedness or flatness of a distribution
Explanation: Kurtosis describes how sharply peaked a distribution is relative to the normal curve: mesokurtic matches the normal, leptokurtic is more peaked with heavier tails, and platykurtic is flatter. ASYMMETRY is skewness, a different concept - the two together describe the shape once location and dispersion are known.
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Question 396
A leptokurtic distribution is one whose curve is:
Select an option first.
Correct answer: B — More peaked than the normal curve
Explanation: Lepto means slender: the curve rises to a sharper peak with heavier tails than the normal. Platykurtic is flatter and mesokurtic matches the normal exactly. Kurtosis says nothing about symmetry, so a leptokurtic curve may still be skewed - which is what distractor D assumes wrongly.
Question 397
Index numbers are best described as:
Select an option first.
Correct answer: C — Specialised averages that measure change approximately
Explanation: An index rests on a sample of items, a chosen base, a set of weights and a formula, and a different reasonable choice at any of those four points would give a different figure. They are therefore indicators of the general trend rather than exact measurements - a limitation worth stating in any theory answer.
Question 398
The median of a grouped frequency distribution is located using:
Select an option first.
Correct answer: B — The cumulative frequency
Explanation: The median class is the one in which the (n/2)th observation falls, which is found by running down the cumulative frequency column; interpolation within that class then gives the value. The highest frequency locates the MODAL class instead, and confusing the two is the standard error in this topic.
Question 399
A fair die is thrown once. The expected value of the number shown is:
Select an option first.
Correct answer: A — 3.5
Explanation: Expectation is the sum of each value multiplied by its probability: (1 + 2 + 3 + 4 + 5 + 6) x 1/6 = 21/6 = 3.5. The expected value need not be an outcome that can actually occur - a point worth stating in a written answer, since it shows expectation is a long-run average rather than a prediction of any single throw.
Question 400
For a binomial distribution with n = 8 and p = 0.5, the mean and variance are respectively:
Select an option first.
Correct answer: C — 4 and 2
Explanation: Mean = np = 4 and variance = npq = 8 x 0.5 x 0.5 = 2. The variance of a binomial is always smaller than its mean, since q is below 1 - so any option showing them equal, as distractor A does, is impossible for a binomial.
Question 401
The mean deviation about the mean of the values 2, 4, 6, 8 and 10 is:
Select an option first.
Correct answer: D — 2.4
Explanation: The mean is 6; the absolute deviations are 4, 2, 0, 2 and 4, totalling 12; dividing by 5 gives 2.4. The absolute signs matter: without them the deviations from the mean always sum to zero, which is precisely why mean deviation is defined on absolute values and standard deviation on squares.
Question 402
The mean deviation about the median of the values 10, 20, 30, 40 and 50 is:
Select an option first.
Correct answer: D — 12
Explanation: The median is 30 and the absolute deviations are 20, 10, 0, 10 and 20, totalling 60; dividing by 5 gives 12. Because the mean here also equals 30, the mean deviation about the mean is the same - but in a skewed data set the figure about the median would be the smaller of the two.
Question 403
In a normal distribution, the mean deviation is approximately what fraction of the standard deviation?
Select an option first.
Correct answer: A — 4/5
Explanation: Mean deviation is about four-fifths, or 0.7979, of the standard deviation in a normal distribution. Together with the quartile deviation at two-thirds, this gives the standard 10 : 12 : 15 ratio. The standard deviation is always the largest of the three, which is a useful check on any computed set.
Question 404
For a binomial distribution with n = 6 and p = 1/2, the mean is:
Select an option first.
Correct answer: C — 3
Explanation: The mean is np = 6 x 0.5 = 3. The variance would be npq = 6 x 0.5 x 0.5 = 1.5, which is distractor A - the two are easily transposed. With p equal to q the distribution is symmetrical about this mean of 3.
Question 405
For a frequency distribution the sum of fx is 3,600 and the sum of f is 80. The arithmetic mean is:
Select an option first.
Correct answer: A — 45
Explanation: The mean of grouped data is the sum of fx divided by the sum of f = 3,600 / 80 = 45. Here x is the class mark of each class and f its frequency. Where the class marks are large or awkward, the step deviation method gives the same answer with much smaller arithmetic - the mean is unaffected by the assumed mean chosen.
Question 406
The arithmetic mean of the first 10 natural numbers is:
Select an option first.
Correct answer: C — 5.5
Explanation: The sum of 1 to 10 is 10 x 11 / 2 = 55, and dividing by 10 gives 5.5. In general the mean of the first n natural numbers is (n + 1)/2. Distractor D is the total rather than the mean - a slip that a moment's plausibility check would catch, since a mean cannot exceed the largest observation.
Question 407
The median of the values 8, 12, 15, 19, 22 and 27 is:
Select an option first.
Correct answer: D — 17
Explanation: With an even number of observations the median is the average of the two middle values once arranged in order: (15 + 19)/2 = 17. The data are already in ascending order here, but arranging them is the essential first step and is where marks are lost when the question presents them jumbled.
Question 408
In a moderately skewed distribution the mean is 24 and the mode is 18. The median is:
Select an option first.
Correct answer: C — 22
Explanation: Rearranging Mode = 3 Median - 2 Mean gives 18 = 3 Median - 48, so the median is 22. As expected for a positively skewed distribution, the median lies BETWEEN the mode and the mean - and nearer the mean, at roughly two-thirds of the way, which the empirical relation encodes.
Question 409
In a symmetrical distribution Q1 is 20 and Q3 is 40. The median is:
Select an option first.
Correct answer: B — 30
Explanation: Symmetry places the median exactly midway between the two quartiles, at (20 + 40)/2 = 30. In a skewed distribution this would not hold, and the gap between the median and each quartile is precisely what Bowley's coefficient of skewness measures.
Question 410
The median of the values 4, 8, 15, 16, 23 and 42 is:
Select an option first.
Correct answer: B — 15.5
Explanation: With six observations already in ascending order, the median is the average of the third and fourth values: (15 + 16)/2 = 15.5. Note that the median need not be one of the observations. Distractor D is the arithmetic mean, which is pulled upward by the extreme value 42.
Question 411
The median of 3, 7, 9, 11 and 15 is:
Select an option first.
Correct answer: C — 9
Explanation: With an odd count the median is the middle value once the data are arranged in order - the third of five, which is 9. For an even count it would be the average of the two middle values. Arranging the data in order is the step candidates skip when the figures already look sorted, and the one the examiner tests by presenting them jumbled.
Question 412
The sum of the squares of the deviations of a set of observations is least when the deviations are measured from:
Select an option first.
Correct answer: C — The arithmetic mean
Explanation: The arithmetic mean minimises the sum of SQUARED deviations - the property on which least squares regression rests. The median has the parallel property for ABSOLUTE deviations, minimising the mean deviation. Keep the two straight: squares point to the mean, absolute values to the median.
Question 413
The mode of the values 4, 5, 5, 6, 7, 5 and 8 is:
Select an option first.
Correct answer: C — 5
Explanation: The mode is the value occurring most often, and 5 appears three times against once for each of the others. Distractor B is the arithmetic mean. A distribution may have no mode at all, or more than one, which is the chief practical limitation of this measure.
Question 414
In a grouped frequency distribution, the modal class is the class having:
Select an option first.
Correct answer: B — The highest frequency
Explanation: The mode is the value occurring most often, so the modal class is simply the one with the greatest frequency; interpolation within it then gives the mode itself. The highest CUMULATIVE frequency always belongs to the last class, which says nothing about where the peak lies - that is the trap in the third option.
Question 415
The most widely used measure of dispersion is the:
Select an option first.
Correct answer: D — Standard deviation
Explanation: Standard deviation uses every observation, is amenable to further algebraic treatment - combined standard deviations, for instance - and underlies the normal distribution and the whole of sampling theory. The range uses only two values and mean deviation, relying on absolute values, is awkward to manipulate algebraically.
Question 416
If A and B are mutually exclusive events, then P(A and B) is:
Select an option first.
Correct answer: C
Explanation: Mutually exclusive means the events cannot occur together, so their intersection is empty and its probability is zero. It follows that the addition rule simplifies to P(A or B) = P(A) + P(B), with no overlap to subtract. Distractor B would apply to INDEPENDENT events, which is a different relationship entirely.
Question 417
Two events with non-zero probabilities that are mutually exclusive:
Select an option first.
Correct answer: C — Cannot be independent
Explanation: If they are mutually exclusive, the occurrence of one makes the other impossible - which is the strongest possible dependence. Formally P(A and B) = 0, whereas independence would require it to equal P(A) x P(B), a positive number. The two ideas are often confused but are close to opposites.
Question 418
Non-sampling errors:
Select an option first.
Correct answer: B — Occur in both sample surveys and a census
Explanation: Non-sampling errors arise from faulty questionnaires, wrong measurement, non-response and processing mistakes, so they afflict a complete census just as much as a sample - often more, since the volume of work is greater. Only SAMPLING error shrinks as the sample grows; non-sampling error may well increase.
Question 419
In a normal distribution, the proportion of observations lying within one standard deviation of the mean is approximately:
Select an option first.
Correct answer: A — 68.27%
Explanation: The empirical rule gives roughly 68.27% within one standard deviation, 95.45% within two and 99.73% within three. These three figures are worth memorising exactly, since they are asked directly and also underlie confidence intervals and control limits in later papers. The normal curve is symmetrical about the mean, where the mean, median and mode coincide.
Question 420
The number of classes in a frequency distribution is conventionally kept between:
Select an option first.
Correct answer: A — 5 and 20
Explanation: Too few classes conceal the shape of the distribution by lumping unlike values together; too many leave the frequencies so thin that no pattern emerges. Five to twenty is the usual working range, with the class interval chosen as the range divided by the intended number of classes.
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