UGC NET Commerce Business Statistics and Research Methods Syllabus

Business Statistics and Research Methods syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Business Statistics and Research Methods in UGC NET Commerce, not a summary of it.

1. 1

   Measures of Central Tendency

   3 topics

   • Mean
   • Median
   • Mode
2. 2

   Measures of Dispersion

   3 topics

   • Range
   • Variance
   • Standard Deviation
3. 3

   Measures of Skewness

   3 topics

   • Positive Skewness
   • Negative Skewness
   • Zero Skewness
4. 4

   Correlation and Regression of Two Variables

   2 topics

   • Correlation Coefficient
   • Regression Analysis
5. 5

   Probability

   2 topics

   • Approaches to Probability
   • Bayes’ Theorem
6. 6

   Probability Distributions

   3 topics

   • Binomial Distribution
   • Poisson Distribution
   • Normal Distribution
7. 7

   Research

   2 topics

   • Concept and Types
   • Research Designs
8. 8

   Data

   2 topics

   • Collection of Data
   • Classification of Data
9. 9

   Sampling and Estimation

   6 topics

   • Concepts
   • Methods of Sampling
     • Probability Methods
     • Non-Probability Methods
   • Sampling Distribution
   • Central Limit Theorem
   • Standard Error
   • Statistical Estimation
10. 10

    Hypothesis Testing

    7 topics

    • z-test
    • t-test
    • ANOVA
    • Chi-square Test
    • Mann-Whitney Test (U-test)
    • Kruskal-Wallis Test (H-test)
    • Rank Correlation Test
11. 11

    Report Writing

    3 topics

    • Structure of a Report
    • Elements of a Report
    • Formatting Guidelines

Business Statistics and Research Methods flashcards for UGC NET Commerce

20 of 51 cards from the Business Statistics and Research Methods deck — real questions with worked answers.

1. What is the arithmetic mean and how is it calculated for ungrouped data?

   The arithmetic mean is the sum of all observations divided by the number of observations: Mean = ΣX / N. It is the most common measure of central tendency but is sensitive to extreme values (outliers).

2. Define the median and state how to locate it in an ordered data set.

   The median is the middle value of data arranged in ascending/descending order. For N observations its position = (N+1)/2 th item. If N is even, it is the average of the two middle values. It is unaffected by extreme values.

3. What is the mode, and what is the empirical relationship linking mean, median and mode?

   The mode is the value occurring most frequently in a data set. The empirical relationship is: Mode = 3 Median − 2 Mean (valid for moderately skewed distributions).

4. Define range as a measure of dispersion and give its coefficient.

   Range = Largest value (L) − Smallest value (S). It is the simplest measure of dispersion. Coefficient of Range = (L − S) / (L + S). It is easy to compute but ignores the distribution of values between extremes.

5. What is variance and how is it computed for a population?

   Variance is the mean of the squared deviations from the arithmetic mean. Population variance σ² = Σ(X − μ)² / N. It measures average squared dispersion; sample variance divides by (n − 1).

6. Define standard deviation and state its relationship to variance.

   Standard deviation (σ) is the positive square root of the variance: σ = √[Σ(X − μ)²/N]. It is the most widely used absolute measure of dispersion, expressed in the same units as the data.

7. What is the coefficient of variation and what is it used for?

   Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100. It is a relative, unit-free measure used to compare variability between two or more data sets; the series with lower CV is more consistent/stable.

8. Describe positive (right) skewness and the order of its mean, median and mode.

   In positive skewness the longer tail is on the right side. Here Mean > Median > Mode. Most values cluster on the left with a few large extreme values pulling the mean upward.

9. Describe negative (left) skewness and the order of its mean, median and mode.

   In negative skewness the longer tail is on the left side. Here Mean < Median < Mode. Most values cluster on the right with a few small extreme values pulling the mean downward.

10. What characterises zero (symmetrical) skewness?

    In a symmetrical distribution skewness = 0, the curve is bell-shaped, and Mean = Median = Mode. The two tails are mirror images of each other (e.g., the normal distribution).

11. State Karl Pearson's coefficient of correlation and its range of values.

    r = Σ(X−X̄)(Y−Ȳ) / [√Σ(X−X̄)² · √Σ(Y−Ȳ)²]. It measures linear association between two variables and ranges from −1 (perfect negative) through 0 (no linear correlation) to +1 (perfect positive).

12. What is the coefficient of determination (r²) and what does it indicate?

    r² is the square of the correlation coefficient. It indicates the proportion of variation in the dependent variable that is explained by the independent variable. For example r = 0.8 gives r² = 0.64, i.e., 64% of variation explained.

13. What is regression analysis and how does it differ from correlation?

    Regression analysis estimates the functional relationship to predict the value of a dependent variable from one or more independent variables. Unlike correlation (which only measures degree/direction of association), regression establishes cause-effect form and allows prediction.

14. Write the two regression equations and the relationship between the regression coefficients and r.

    Regression of Y on X: Y − Ȳ = byx (X − X̄); regression of X on Y: X − X̄ = bxy (Y − Ȳ). The correlation coefficient r = √(byx × bxy), and r carries the same sign as the regression coefficients.

15. List the three main approaches/definitions of probability.

    (1) Classical (a priori) approach: P = favourable outcomes / total equally likely outcomes; (2) Relative frequency (empirical) approach: based on observed long-run frequency; (3) Subjective approach: based on personal judgement/degree of belief.

16. State Bayes' Theorem formula and its purpose.

    P(Aᵢ|B) = [P(Aᵢ) · P(B|Aᵢ)] / Σ[P(Aⱼ) · P(B|Aⱼ)]. It revises (updates) prior probabilities into posterior probabilities given new evidence B, using conditional probabilities.

17. Define the binomial distribution and give its probability function, mean and variance.

    It models the number of successes in n independent Bernoulli trials with constant success probability p. P(X=r) = ⁿCr pʳ q^(n−r) where q = 1−p. Mean = np; Variance = npq (so variance < mean).

18. Define the Poisson distribution, its probability function, mean and variance.

    It models the number of rare events in a fixed interval. P(X=x) = (e^−λ · λˣ)/x!, where λ is the average rate. Its key property is Mean = Variance = λ. It is the limiting case of the binomial when n→∞ and p→0.

19. List the main properties of the normal distribution.

    It is symmetrical and bell-shaped; Mean = Median = Mode; the curve is asymptotic to the X-axis; total area under the curve = 1; it is fully defined by μ and σ; and it follows the empirical (68-95-99.7) rule.

20. State the empirical rule (68-95-99.7) for the normal distribution.

    Approximately 68.27% of observations lie within μ ± 1σ, about 95.45% within μ ± 2σ, and about 99.73% within μ ± 3σ. This is the basis for setting confidence limits.

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