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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 451
Which of the following is a property of the arithmetic mean?
Select an option first.
Correct answer: A — The sum of the deviations from it is zero
Explanation: The deviations above and below the mean cancel exactly, which is the balancing-point property and the reason mean deviation uses absolute values. The mean IS affected by extreme values, cannot be read from an ogive, and exists for any set of numerical data whatever its shape.
Question 452
The coefficient of correlation is independent of:
Select an option first.
Correct answer: A — Both the change of origin and the change of scale
Explanation: Because it is a ratio of comparable quantities, r is unaffected by adding a constant to every value or by multiplying every value by a positive constant - which is precisely why the shortcut method using assumed means and common factors is valid. Regression COEFFICIENTS, by contrast, are independent of origin but NOT of scale.
Question 453
The normal distribution is:
Select an option first.
Correct answer: A — Symmetrical and bell-shaped, with mean, median and mode all equal
Explanation: The normal curve is symmetrical about its mean, bell-shaped, and asymptotic to the horizontal axis in both directions, so it extends over all real values rather than a bounded range. Its symmetry makes the mean, median and mode coincide, and it is CONTINUOUS - the binomial and Poisson are the discrete distributions.
Question 454
The algebraic sum of the deviations of a set of observations from their arithmetic mean is always:
Select an option first.
Correct answer: C — Zero
Explanation: The mean is the balancing point of the data, so positive and negative deviations exactly offset one another and the sum is zero. This property is why the mean deviation is defined on ABSOLUTE deviations and the variance on SQUARED ones - without one of those devices the measure would collapse to zero for every data set.
Question 455
The chief practical use of a cost of living index is to:
Select an option first.
Correct answer: C — Adjust wages and allowances for changes in the price level
Explanation: The index is used to compute dearness allowance and to convert money wages into real wages, so that purchasing power is maintained as prices change. It is constructed for a specific class of consumers from a family budget enquiry, which is why a single national figure would not serve.
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Question 456
Stratified sampling is used when the population is:
Select an option first.
Correct answer: D — Heterogeneous but divisible into homogeneous groups
Explanation: The population is divided into strata that are internally similar but differ from one another, and a sample is drawn from each. This guarantees representation of every stratum and generally yields a smaller sampling error than simple random sampling on a heterogeneous population.
Question 457
If the first quartile is 24 and the third quartile is 42, the quartile deviation is:
Select an option first.
Correct answer: B — 9
Explanation: Quartile deviation, also called the semi-interquartile range, is (Q3 - Q1)/2 = (42 - 24)/2 = 9. Distractor A is the interquartile range, which is the full difference - the word SEMI is what halves it. Being based on the middle half of the data, this measure is unaffected by extreme values at either end.
Question 458
If Q1 is 15 and Q3 is 35, the quartile deviation and its coefficient are respectively:
Select an option first.
Correct answer: D — 10 and 0.40
Explanation: Quartile deviation = (35 - 15)/2 = 10, and the coefficient = (35 - 15)/(35 + 15) = 20/50 = 0.40. The first is an ABSOLUTE measure in the units of the data; the second is a pure number allowing comparison between distributions. Distractor A gives the interquartile range instead of the semi-interquartile range.
Question 459
In a normal distribution, the quartile deviation is approximately what fraction of the standard deviation?
Select an option first.
Correct answer: A — 2/3
Explanation: For a normal distribution QD is approximately two-thirds of the standard deviation, and mean deviation about four-fifths of it - giving the ratio QD : MD : SD of roughly 10 : 12 : 15. These relationships let one measure of dispersion be estimated from another and are directly examinable.
Question 460
In a normal distribution the first and third quartiles are located at:
Select an option first.
Correct answer: C — The mean plus or minus 0.6745 standard deviations
Explanation: The quartiles cut off 25% in each tail, which occurs at 0.6745 standard deviations from the mean. This is why the quartile deviation is about two-thirds of the standard deviation, and it is also the multiplier that appears in the formula for probable error.
Question 461
The range of the values 12, 18, 25, 9, 31 and 14 is:
Select an option first.
Correct answer: A — 22
Explanation: Range = largest value minus smallest value = 31 - 9 = 22. It is the simplest measure of dispersion but uses only two observations and is therefore highly sensitive to an extreme value - which is why quartile deviation or standard deviation is preferred when the data contain outliers.
Question 462
Karl Pearson's coefficient of correlation always lies between:
Select an option first.
Correct answer: C — -1 and +1
Explanation: The coefficient ranges from -1, a perfect inverse linear relationship, through 0, no linear relationship, to +1, a perfect direct one. Any computed value outside that range signals an arithmetical error. The SIGN shows the direction of the relationship and the magnitude its strength - two separate pieces of information.
Question 463
For 10 pairs of ranks the sum of the squares of the differences is 30. The coefficient of rank correlation is:
Select an option first.
Correct answer: B — 0.818
Explanation: Spearman's coefficient = 1 - [6 x sum of d squared] / [n(n squared - 1)] = 1 - (6 x 30)/(10 x 99) = 1 - 0.1818 = 0.818. A small sum of squared rank differences means the two rankings largely agree, so a high positive value is expected - distractor A is what results from forgetting to subtract from 1.
Question 464
Sampling error can generally be reduced by:
Select an option first.
Correct answer: A — Increasing the size of the sample
Explanation: A larger sample represents the population more closely, so the estimate varies less from sample to sample - the standard error falls in proportion to the square root of the sample size. The other options introduce BIAS, which is a different and more dangerous defect, since unlike sampling error it does not shrink as the sample grows.
Question 465
The two regression coefficients:
Select an option first.
Correct answer: B — Always carry the same sign, which is the sign of the correlation
Explanation: Both coefficients take their sign from the covariance, so they must agree with each other and with the correlation coefficient. A question presenting one positive and one negative coefficient describes impossible data - a validity check worth applying whenever both are supplied.
Question 466
The two regression lines are 2x + 3y = 8 and 4x + y = 10. The mean values of x and y are:
Select an option first.
Correct answer: A — x = 2.2 and y = 1.2
Explanation: The two regression lines always intersect at the point of means, so solving them simultaneously gives the answer: from the second, y = 10 - 4x; substituting, 2x + 30 - 12x = 8, so x = 2.2 and y = 1.2. This property is what makes the question solvable at all - no data are needed beyond the two equations.
Question 467
The relative frequency of a class is its frequency divided by:
Select an option first.
Correct answer: B — The total frequency
Explanation: Relative frequency expresses each class as a proportion of the whole, so the relative frequencies of all classes sum to 1, or to 100 when written as percentages. Dividing by the class WIDTH gives frequency density instead, which is what a histogram needs when class widths are unequal.
Question 468
A sampling frame is:
Select an option first.
Correct answer: D — The list of all units in the population from which the sample is drawn
Explanation: The frame is the complete list - an electoral roll or a register of members, for instance - from which units are selected. An incomplete or out-of-date frame produces bias that no amount of random selection can correct, because units missing from the frame have no chance of selection at all.
Question 469
A sampling method in which every member of the population has an equal chance of being selected is:
Select an option first.
Correct answer: A — Simple random sampling
Explanation: Simple random sampling gives every unit an equal and independent chance of selection, which is what makes the sampling error measurable and the results generalisable. Quota, judgement and convenience sampling are all NON-probability methods that rely on the investigator's choice, so no valid estimate of sampling error can be made from them.
Question 470
A scatter diagram is used to:
Select an option first.
Correct answer: B — Give a first visual impression of the relationship between two variables
Explanation: Plotting the paired observations reveals at a glance whether the association is positive, negative or absent, and whether it is linear - which matters, because the correlation coefficient measures only LINEAR association. Drawing the scatter first is what prevents a meaningless r being computed on curved data.
Question 471
In a less-than ogive, the curve is:
Select an option first.
Correct answer: A — Rising from left to right
Explanation: Cumulative frequencies can only accumulate, so a less-than ogive never falls - it rises from zero to the total frequency. A MORE-than ogive does the reverse, falling from the total to zero, and the point where the two cross gives the median.
Question 472
A box contains 4 white and 6 black balls. One ball is drawn at random. The probability that it is white is:
Select an option first.
Correct answer: A — 2/5
Explanation: There are 10 balls of which 4 are white, so the probability is 4/10 = 2/5. Distractor B is the probability of BLACK, and the two must sum to 1 - a check worth making. Count the total, not just the favourable cases, before forming the fraction.
Question 473
Splicing of index numbers means:
Select an option first.
Correct answer: D — Joining two index series with different base years into one continuous series
Explanation: When an index is rebased, the old and new series can be linked by multiplying one of them by the ratio of the overlapping figures, producing a single comparable series. It is what allows a long run of data to survive a change of base year, and it is examined alongside base shifting and deflating.
Question 474
If the variance of a distribution is 49, the standard deviation is:
Select an option first.
Correct answer: C — 7
Explanation: Standard deviation is the positive square root of the variance, so it is 7. Distractor B is the variance squared. The standard deviation is always in the same units as the original data, whereas the variance is in squared units - which is why the standard deviation is the measure normally quoted.
Question 475
The standard deviation of the values 5, 5, 5, 5 and 5 is:
Select an option first.
Correct answer: D
Explanation: Every observation equals the mean, so every deviation is zero and the standard deviation is zero. This is the minimum possible value - standard deviation can never be negative, since it is the square root of a mean of squares. A zero standard deviation means no dispersion whatsoever.
Question 476
The standard deviation of the first n natural numbers depends on:
Select an option first.
Correct answer: C — n alone
Explanation: The values 1 to n are fully determined by n, so every statistic computed from them - including the standard deviation, which works out as the square root of (n squared - 1)/12 - is a function of n only. Recognising that the data are completely specified by one parameter is the insight the question tests.
Question 477
The standard error of a sample mean measures:
Select an option first.
Correct answer: B — The variability of the sample mean from sample to sample
Explanation: The standard error is the standard deviation of the sampling distribution, showing how much the estimate would vary if the survey were repeated. It equals the population standard deviation divided by the square root of n, so it falls as the sample grows - unlike bias, which does not.
Question 478
The standard normal variate z is defined as:
Select an option first.
Correct answer: D — (x minus the mean) divided by the standard deviation
Explanation: Subtracting the mean shifts the distribution to a centre of zero and dividing by the standard deviation rescales it to a spread of one, producing a standard normal distribution with mean 0 and variance 1. This standardisation is what allows a single published table to serve every normal distribution whatever its parameters.
Question 479
For a perfectly symmetrical distribution, the mean, median and mode are:
Select an option first.
Correct answer: B — All equal
Explanation: Symmetry means the two halves of the distribution mirror each other, so the balancing point (mean), the middle value (median) and the peak (mode) all fall at the same point. Any divergence between the three is a measure of skewness - which is why Pearson's coefficient of skewness is built on the difference between mean and mode.
Question 480
In a binomial distribution, when p equals q the distribution is:
Select an option first.
Correct answer: C — Symmetrical
Explanation: When p = q = 0.5 the probabilities of x successes and of (n - x) successes are equal, so the distribution is symmetrical about its mean of n/2. It is positively skewed when p is less than 0.5 and negatively skewed when p exceeds 0.5, and it approaches the normal curve as n grows large.
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