SSC CGL (Combined Graduate Level) Statistics (Tier II Paper II) Syllabus

Statistics (Tier II Paper II) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Statistics (Tier II Paper II) in SSC CGL (Combined Graduate Level), not a summary of it.

1. 1

   Collection and Presentation of Data

   4 topics

   • Primary and Secondary Data
   • Methods of Data Collection and Sampling
   • Classification and Tabulation
   • Graphical Representation
     • Histogram and frequency polygon
     • Ogives and frequency curves
2. 2

   Measures of Central Tendency and Dispersion

   3 topics

   • Mean, Median and Mode
     • Arithmetic, geometric and harmonic mean
     • Partition values: quartiles, deciles, percentiles
   • Measures of Dispersion
     • Range and mean deviation
     • Standard deviation and variance
   • Moments, Skewness and Kurtosis
3. 3

   Correlation, Regression and Index Numbers

   4 topics

   • Correlation Analysis
     • Karl Pearson coefficient
     • Spearman rank correlation
   • Regression Analysis and Lines of Regression
   • Index Numbers
     • Construction and types
     • Tests of consistency and cost of living index
   • Time Series Analysis
     • Components of time series
     • Trend measurement methods
4. 4

   Probability and Theoretical Distributions

   4 topics

   • Probability Theory and Theorems
   • Random Variables and Mathematical Expectation
   • Theoretical Distributions
     • Binomial and Poisson distributions
     • Normal distribution
   • Sampling and Statistical Inference
     • Sampling distributions and standard error
     • Estimation and tests of hypothesis

Statistics (Tier II Paper II) flashcards for SSC CGL (Combined Graduate Level)

20 of 61 cards from the Statistics (Tier II Paper II) deck — real questions with worked answers.

1. What is the difference between primary data and secondary data?

   Primary data is collected first-hand by the investigator for a specific purpose (original, fresh). Secondary data is already collected by someone else and reused (already exists, e.g., census reports, journals).

2. List the main methods of collecting primary data.

   Direct personal investigation, indirect oral investigation, information through correspondents, mailed questionnaire, and schedules sent through enumerators.

3. What is the difference between a questionnaire and a schedule?

   A questionnaire is filled in by the respondent themselves; a schedule is filled in by an enumerator who asks the respondent the questions.

4. What is the difference between census and sampling methods of data collection?

   Census surveys every unit of the population (complete enumeration); sampling studies only a representative subset and infers about the whole population.

5. What is the difference between probability (random) sampling and non-probability sampling?

   In probability sampling every unit has a known, non-zero chance of selection (e.g., simple random, stratified). In non-probability sampling selection is based on judgment/convenience and chances are unknown (e.g., quota, judgment, convenience).

6. In statistics, what are sampling errors and non-sampling errors?

   Sampling error arises because only a sample (not whole population) is studied; it decreases as sample size increases. Non-sampling error arises from faulty data collection, measurement, or processing and can occur in both census and sampling.

7. Define stratified sampling.

   The population is divided into homogeneous non-overlapping groups (strata), and a random sample is drawn from each stratum, ensuring representation of every group.

8. What is systematic sampling?

   Units are selected at regular intervals from an ordered list; after a random start, every k-th unit is chosen, where k = N/n (population size / sample size).

9. What is the difference between classification and tabulation?

   Classification arranges data into homogeneous groups/classes based on common characteristics; tabulation presents the classified data systematically in rows and columns of a table.

10. Name the four main bases of classification of data.

    Geographical (spatial), chronological (time), qualitative (attributes), and quantitative (numerical/variable) classification.

11. What is the difference between a discrete and a continuous variable?

    A discrete variable takes only specific separate values (e.g., number of children); a continuous variable can take any value within a range (e.g., height, weight).

12. In a frequency distribution, what is the class mark (mid-value) and how is it computed?

    The class mark is the midpoint of a class interval, computed as (lower limit + upper limit) / 2.

13. What is the difference between inclusive and exclusive class intervals?

    In exclusive classes the upper limit of one class equals the lower limit of the next and is excluded from it (e.g., 10-20, 20-30). In inclusive classes both limits belong to the class (e.g., 10-19, 20-29), leaving gaps that need correction for continuity.

14. How do you find the class width (size) and is class boundary correction needed?

    Class width = upper class boundary - lower class boundary. For inclusive classes, correction factor = (lower limit of next class - upper limit of current)/2 is subtracted from lower and added to upper limits to get true boundaries.

15. Which graph is used to represent a cumulative frequency distribution, and what does it determine?

    An ogive (cumulative frequency curve). The 'less than' and 'more than' ogives intersect at the median value.

16. What is the difference between a histogram and a bar diagram?

    A histogram represents continuous frequency data with adjacent bars (no gaps), area proportional to frequency; a bar diagram represents discrete/categorical data with separated bars of equal width whose height shows value.

17. What is a frequency polygon and how is it drawn?

    A frequency polygon is a line graph formed by joining the midpoints (class marks) of the tops of histogram bars with straight lines; the ends are brought down to the axis at the adjacent midpoints.

18. How is the mode located graphically using a histogram?

    Draw the histogram; from the top corners of the highest (modal) rectangle, draw two cross diagonals to the adjacent rectangle tops; drop a perpendicular from their intersection to the x-axis—that point is the mode.

19. State the formula for the arithmetic mean of a frequency distribution.

    Mean = Σ(f·x) / Σf, where x is the value (or class mark) and f is its frequency.

20. State the assumed-mean (shortcut) formula for the arithmetic mean.

    Mean = A + (Σf·d / Σf), where A is the assumed mean and d = x − A is the deviation from the assumed mean.

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