CA Foundation PAPER 3: QUANTITATIVE APTITUDE Flashcards

24 sample cards from the PAPER 3: QUANTITATIVE APTITUDE deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. In blood relation problems, who is your father's father's only son, and your mother's brother?

   Father's father's only son = your father. Mother's brother = your maternal uncle. (Key skill: break the chain step by step and track gender.)

2. What are the main forms of statistical (graphical) representation of data?

   Bar diagram, pie chart (circular diagram), histogram, frequency polygon, ogive (cumulative frequency curve), and line/time-series graphs. Tabulation and textual presentation are non-graphical forms.

3. What is the difference between an inclusive and an exclusive class interval?

   Exclusive: upper limit of one class equals lower limit of next (e.g., 10–20, 20–30); upper limit not included. Inclusive: limits do not overlap (e.g., 10–19, 20–29); must be converted to exclusive (class boundaries) before drawing a histogram.

4. Distinguish between a census and a sample survey.

   Census: data collected from every unit of the entire population (complete enumeration). Sample survey: data collected from a representative subset (sample) of the population, then generalized. Sampling saves time and cost but has sampling error.

5. Differentiate between a parameter and a statistic.

   A parameter is a numerical characteristic of the population (e.g., population mean μ, population SD σ). A statistic is a numerical characteristic computed from a sample (e.g., sample mean x̄, sample SD s) used to estimate the parameter.

6. Name common probability/random sampling methods.

   Simple random sampling (with/without replacement), stratified sampling, systematic sampling, cluster sampling, and multistage sampling. These are probability sampling methods; quota and convenience sampling are non-probability methods.

7. State the formulas for Mean, Median (for grouped data), and Mode.

   Mean = Σfx/Σf. Median (grouped) = L + [(N/2 − cf)/f] × h. Mode = most frequent value; grouped Mode = L + [(f1−f0)/(2f1−f0−f2)] × h.

8. State the empirical relationship between Mean, Median, and Mode.

   Mode = 3 Median − 2 Mean (for a moderately asymmetrical/skewed distribution). For a perfectly symmetrical distribution, Mean = Median = Mode.

9. What are the main measures of dispersion?

   Range, Quartile Deviation (semi-interquartile range), Mean Deviation, Standard Deviation, and Variance. Range and QD are absolute measures based on position; SD and MD are based on all values.

10. State the formula for Standard Deviation and Variance for a frequency distribution.

    Variance σ² = Σf(x − x̄)²/N = Σfx²/N − (Σfx/N)². Standard Deviation σ = √(Variance). SD is the positive square root of variance.

11. What is the Coefficient of Variation and what does it indicate?

    CV = (Standard Deviation / Mean) × 100. It is a relative measure of dispersion used to compare variability of two or more series; a higher CV means less consistency/more variability.

12. State the classical (mathematical) definition of probability.

    P(A) = (Number of favourable outcomes) / (Total number of equally likely outcomes) = m/n. Probability lies between 0 and 1 inclusive.

13. State the addition theorem of probability for two events.

    P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).

14. State the multiplication theorem and the condition for independent events.

    P(A ∩ B) = P(A) × P(B|A). For independent events, P(B|A) = P(B), so P(A ∩ B) = P(A) × P(B).

15. State Bayes' Theorem and conditional probability formula.

    Conditional: P(A|B) = P(A∩B)/P(B). Bayes: P(Ai|B) = [P(Ai)·P(B|Ai)] / Σ[P(Aj)·P(B|Aj)]. It revises prior probabilities using observed evidence.

16. State the mean and variance of the Binomial distribution.

    For Binomial B(n, p): Mean = np, Variance = npq (where q = 1−p), Standard Deviation = √(npq). Note: Mean > Variance always (since q < 1).

17. State the conditions/properties of a Binomial distribution.

    Fixed number of trials n; each trial has only two outcomes (success/failure); constant probability p of success; trials are independent. P(X=r) = nCr · p^r · q^(n−r).

18. State the mean and variance of the Poisson distribution.

    For Poisson with parameter m: Mean = Variance = m. P(X = r) = (e^(−m) · m^r)/r!. It is the limiting case of binomial when n→∞, p→0, np = m (rare events).

19. State the key properties of the Normal distribution.

    Bell-shaped and symmetrical about the mean; Mean = Median = Mode; total area = 1; defined by μ and σ. Empirical rule: about 68% of data lie within μ ± σ, 95% within μ ± 2σ, 99.7% within μ ± 3σ.

20. What is the standard normal variate (z-score) and its distribution parameters?

    z = (x − μ)/σ. The standard normal distribution has mean = 0 and standard deviation = 1. The z-score measures how many standard deviations a value is from the mean.

21. What does the correlation coefficient (r) measure and what is its range?

    It measures the degree and direction of linear relationship between two variables. r ranges from −1 to +1: +1 = perfect positive, −1 = perfect negative, 0 = no linear correlation.

22. State the formula for Karl Pearson's coefficient of correlation.

    r = Σ(x−x̄)(y−ȳ) / √[Σ(x−x̄)²·Σ(y−ȳ)²], or r = [nΣxy − ΣxΣy] / √{[nΣx² − (Σx)²][nΣy² − (Σy)²]}.

23. State the formula for Spearman's rank correlation coefficient.

    R = 1 − [6Σd²] / [n(n² − 1)], where d = difference between ranks of paired items and n = number of pairs.

24. What are the two regression coefficients, and how do they relate to r?

    byx = r·(σy/σx) (regression of y on x) and bxy = r·(σx/σy) (regression of x on y). Their product byx × bxy = r², so r = ±√(byx × bxy) (sign same as the regression coefficients).

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PAPER 3: QUANTITATIVE APTITUDE flashcards FAQ