UGC NET Environmental Science Unit-IX: Statistical Approaches and Modelling in Environmental Sciences Syllabus

Unit-IX: Statistical Approaches and Modelling in Environmental Sciences syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Unit-IX: Statistical Approaches and Modelling in Environmental Sciences in UGC NET Environmental Science, not a summary of it.

1. 1

   Unit-IX: Statistical Approaches and Modelling

   8 topics

   • Attributes and Variables
     • Types of variables
     • Scales of measurement
   • Central Tendency and Dispersion
     • Measurement of central tendency
     • Measurement of dispersion
     • Standard error
     • Moments - measure of skewness and kurtosis
   • Probability Theory
     • Basic concepts of probability theory
   • Sampling Theory
     • Sampling techniques
   • Distributions
     • Normal distribution
     • Log-normal distribution
     • Binomial distribution
     • Poisson distribution
     • t-distribution
     • F-distribution
   • Correlation and Regression
     • Correlation analysis
     • Regression analysis
     • Tests of hypothesis (t-test, ANOVA: one-way and two-way)
     • Significance and confidence limits
   • Approaches to Development of Environmental Models
     • Linear regression models
     • Simple regression models
     • Multiple regression models
     • Validation and forecasting
   • Models of Population Growth and Interactions
     • Lotka-Voltera model
     • Leslie’s matrix model

Unit-IX: Statistical Approaches and Modelling in Environmental Sciences flashcards for UGC NET Environmental Science

19 of 53 cards from the Unit-IX: Statistical Approaches and Modelling in Environmental Sciences deck — real questions with worked answers.

1. In statistics, what is the difference between an attribute and a variable?

   An attribute is a qualitative characteristic that cannot be measured numerically (e.g., sex, colour, literacy), studied by presence/absence. A variable is a quantitative characteristic that can be measured and expressed numerically (e.g., height, temperature).

2. Distinguish between discrete and continuous variables with examples.

   A discrete variable takes only isolated/whole values (e.g., number of plants, family size). A continuous variable can take any value within a range, including fractions (e.g., rainfall, temperature, weight).

3. What are the four scales of measurement of data?

   Nominal (labels/categories), Ordinal (ranked categories), Interval (equal intervals, no true zero, e.g., °C), and Ratio (equal intervals with a true zero, e.g., weight, length).

4. What are the three common measures of central tendency?

   Arithmetic Mean, Median, and Mode.

5. State the empirical relationship between mean, median and mode for a moderately skewed distribution.

   Mode = 3 Median − 2 Mean (equivalently, Mean − Mode = 3(Mean − Median)).

6. Which measure of central tendency is most affected by extreme values, and which is unaffected?

   The arithmetic mean is most affected by extreme values; the median (and mode) is unaffected by extreme values.

7. How are the median and mode positioned relative to the mean in a positively (right) skewed distribution?

   In a positive skew: Mean > Median > Mode (the mean is pulled toward the long right tail).

8. What are the main measures of dispersion?

   Range, Quartile Deviation (semi-interquartile range), Mean Deviation, Variance, and Standard Deviation (and the relative measure, Coefficient of Variation).

9. Define standard deviation and give its formula for a population.

   Standard deviation is the positive square root of the mean of squared deviations from the mean. Population SD: σ = √[Σ(x − μ)² / N].

10. What is variance and how does it relate to standard deviation?

    Variance is the mean of the squared deviations from the mean (σ²). Standard deviation is the square root of the variance.

11. What is the Coefficient of Variation (CV) and what is it used for?

    CV = (Standard Deviation / Mean) × 100. It is a relative, unit-free measure used to compare variability/consistency between two or more datasets; a lower CV means greater consistency.

12. Define quartile deviation (semi-interquartile range).

    Quartile Deviation = (Q3 − Q1)/2, where Q1 and Q3 are the first and third quartiles. It measures the spread of the middle 50% of data.

13. What is skewness and what does its sign indicate?

    Skewness measures the asymmetry of a distribution. Positive skewness = long right tail (mean > mode); negative skewness = long left tail (mean < mode); zero = symmetric.

14. What is kurtosis, and name its three types?

    Kurtosis measures the peakedness/flatness of a distribution. Types: Leptokurtic (more peaked, kurtosis >3), Mesokurtic (normal, =3), and Platykurtic (flatter, <3).

15. What are the three classical/axiomatic approaches to defining probability?

    Classical (a priori) probability, Empirical (relative frequency/statistical) probability, and Axiomatic (Kolmogorov) probability.

16. State the classical definition of the probability of an event.

    P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes).

17. State the addition theorem of probability for two events A and B.

    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).

18. State the multiplication theorem of probability for two independent events.

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

19. What is conditional probability and its formula?

    Conditional probability is the probability of event A given that B has occurred: P(A|B) = P(A∩B)/P(B), provided P(B) > 0.

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