UGC NET Environmental Science Unit 9 PYQs, Important Questions

UGC NET Environmental Science Unit 9 PYQs are useful for students preparing the Statistical Approaches section in an exam-focused way. This unit includes topics like mean, median, mode, variance, standard deviation, correlation, regression, probability distributions, hypothesis testing, ANOVA, Chi-square test, t-test, p-value, and confidence interval. 

 Practising previous year questions helps students understand repeated concepts, numerical patterns, and the type of logic used in the exam. Since Unit 9 is formula-based and concept-heavy, regular PYQ practice can improve accuracy, speed, and confidence. These questions are helpful for quick revision and better preparation. 

UGC NET Environmental Science Unit 9 PYQs 

UGC NET Environmental Science Unit 9 PYQs with options and answers help students practise Statistical Approaches in a clear exam-based format. These questions cover important topics like mean, variance, standard deviation, correlation, regression, hypothesis testing, ANOVA, Chi-square test, and probability distributions. Check the questions below for practice and quick revision. 

Q1. The second order moment about mean is equal to:
A. Mean
B. Variance
C. Skewness
D. Kurtosis
Answer: B. Variance

Q2. Arrange the following in increasing range of values they can take:
A. Sum of deviations about mean → Coefficient of correlation → Coefficient of determination → Standard normal variate
B. Coefficient of determination → Sum of deviations about mean → Coefficient of correlation → Standard normal variate
C. Coefficient of correlation → Coefficient of determination → Sum of deviations about mean → Standard normal variate
D. Sum of deviations about mean → Coefficient of determination → Coefficient of correlation → Standard normal variate
Answer: D. Sum of deviations about mean → Coefficient of determination → Coefficient of correlation → Standard normal variate

Q3. Which of the following is most appropriate for visualizing time-sequence data of a variable?
A. Line chart
B. Histogram
C. Box plot
D. Scatter plot
Answer: A. Line chart

Q4. For a set of observations, the relationship among Arithmetic Mean, Geometric Mean, and Harmonic Mean is represented by:
A. AM = GM × HM
B. GM = AM + HM
C. GM² = AM × HM
D. HM² = AM × GM
Answer: C. GM² = AM × HM

Q5. In estimating the correlation coefficient between two variables X and Y, the nature of correlation is determined by:
A. Mean of X
B. Mean of Y
C. Standard deviation
D. Covariance between X and Y
Answer: D. Covariance between X and Y

Q6. F-distribution is used in hypothesis testing for:
A. Comparing variances and comparing more than two population means
B. Calculating correlation coefficient only
C. Inference about one population mean only
D. Calculating median only
Answer: A. Comparing variances and comparing more than two population means

Q7. Identify the models appropriate for univariate data:
A. Logistic regression only
B. Exponential smoothing, moving average, and autoregressive models
C. Logistic regression and moving average
D. Logistic regression and autoregressive models
Answer: B. Exponential smoothing, moving average, and autoregressive models

Q8. If data on a variable is normally distributed with mean 20 and standard deviation 4, the probability that the variable lies between 16 and 24 is:
A. 0.50
B. 0.68
C. 0.82
D. 0.95
Answer: B. 0.68

Q9. If Z represents the standard normal variate, the probability that Z lies between -2 and +1 is approximately:
A. 0.82
B. 0.68
C. 0.95
D. 0.50
Answer: A. 0.82

Q10. Arrange the regression models in increasing order of explanatory power gain:
A. A → B → C → D
B. C → A → B → D
C. D → B → A → C
D. B → C → A → D
Answer: B. C → A → B → D

Q11. When there is very high correlation among independent variables in a multiple linear regression model, it suffers from:
A. Autocorrelation
B. Multicollinearity
C. Homoscedasticity
D. Heteroscedasticity
Answer: B. Multicollinearity

Q12. Arrange the following cases in increasing order of variance for binomial distribution:
A. A → B → C → D
B. B → A → C → D
C. B → C → A → D
D. D → A → C → B
Answer: C. B → C → A → D

Q13. Identify the correct statements:
A. Mean of a standard normal variate is zero
B. Sum of squares of deviations about mean is always maximum
C. In a negatively skewed distribution, Mean < Median < Mode
D. Mean and variance are equal in Poisson distribution
Answer: A, C and D

Q14. Match the statistical tests with their correct applications:
A. Chi-square test — Comparing means of two groups
B. Mann-Whitney test — Comparing median across two groups
C. Z-test — Testing association between categorical variables
D. ANOVA — Comparing proportions only
Answer: B. Mann-Whitney test — Comparing median across two groups

Q15. Correct sequence of steps in one-way ANOVA is:
A. Tabulate data → Partition variance → Find degrees of freedom → Calculate mean sum of squares → Calculate F-ratio
B. Find degrees of freedom → Tabulate data → Calculate F-ratio → Partition variance
C. Calculate F-ratio → Tabulate data → Find degrees of freedom
D. Partition variance → Calculate F-ratio → Tabulate data
Answer: A. Tabulate data → Partition variance → Find degrees of freedom → Calculate mean sum of squares → Calculate F-ratio

Q16. Which statements are true about t-distribution in hypothesis testing?
A. It is non-parametric
B. It tests whether sample mean differs significantly from population mean
C. It can be used with correlation coefficient
D. It is used only for covariance
Answer: B and C

Q17. Which statements are true for testing statistical hypothesis?
A. There are two hypotheses: null and alternative
B. Both hypotheses can be accepted at the same time
C. Critical value always lies in the acceptance region
D. If one hypothesis is rejected, the other is accepted
Answer: A and D

Q18. Arrange the steps for assessing model fitness:
A. Calculate residual values → Estimate constants → Assess residual mean
B. Estimate constants → Calculate residual values → Assess fitted and given dependent variable means → Estimate residual mean → Assess residual mean
C. Assess residual mean → Estimate constants → Calculate residual values
D. Estimate residual mean → Calculate residual values → Estimate constants
Answer: B. Estimate constants → Calculate residual values → Assess fitted and given dependent variable means → Estimate residual mean → Assess residual mean

Q19. Standard error of mean for normally distributed data on 256 observations is 0.1. If mean is 60, the possible limits covering 95% observations are:
A. 58.8 and 61.2
B. 56.8 and 63.2
C. 55.8 and 64.2
D. 57.5 and 62.5
Answer: B. 56.8 and 63.2

Q20. Correct sequence for Chi-square test of association is:
A. Calculate Chi-square → Set hypothesis → Compare values
B. Set null hypothesis → Prepare contingency table → Calculate expected frequencies → Apply formula → Compare calculated and table values
C. Prepare table → Calculate mean → Calculate standard deviation
D. Set alternative hypothesis → Calculate regression coefficient
Answer: B. Set null hypothesis → Prepare contingency table → Calculate expected frequencies → Apply formula → Compare calculated and table values

Q21. In a frequency distribution table with equally spaced class intervals, which measure of central tendency requires three class interval frequencies for estimation?
A. Mean
B. Median
C. Mode
D. Range
Answer: C. Mode

Q22. Which condition is false for the validity of Chi-square test as a goodness of fit test?
A. Observations should be independent
B. Data should be frequency data
C. Expected frequency should be sufficiently large
D. Cell frequency should be less than 5
Answer: D. Cell frequency should be less than 5

Q23. Match the following correctly:
A. Central tendency — Degree of closeness; Dispersion — Degree of spreadness; Skewness — Tail/asymmetry; Kurtosis — Peakness
B. Central tendency — Peakness; Dispersion — Tail; Skewness — Spreadness
C. Central tendency — Spreadness; Kurtosis — Closeness
D. Dispersion — Peakness; Skewness — Mean
Answer: A. Central tendency — Degree of closeness; Dispersion — Degree of spreadness; Skewness — Tail/asymmetry; Kurtosis — Peakness

Q24. The functional relationship of soil expressed in terms of several factors is best represented by:
A. Simple correlation
B. Simple linear regression
C. Multiple linear regression model
D. Logistic regression only
Answer: C. Multiple linear regression model

Q25. Which are correct representations of standard deviation?
A. √[Σ(x - x̄)² / n]
B. √[Σx²/n - (Σx/n)²]
C. Both A and B
D. Σx/n
Answer: C. Both A and B

Q26. For a moderately asymmetrical distribution, mean, median and mode obey which relationship?
A. Mean = Median = Mode
B. Mode = 3 Median - 2 Mean
C. Mean - Median = 1/3 (Mean - Mode)
D. Both B and C
Answer: D. Both B and C

Q27. Correct sequence for calculating a 95% confidence interval using moving average rainfall data is:
A. Calculate error → Plot graph → Choose confidence coefficient → Apply formula
B. Plot time series graph → Calculate average → Calculate error → Choose confidence coefficient → Apply t-statistic formula
C. Choose confidence coefficient → Plot graph → Calculate average
D. Apply formula → Calculate error → Plot graph
Answer: B. Plot time series graph → Calculate average → Calculate error → Choose confidence coefficient → Apply t-statistic formula

Q28. Statement 1: Past data record helps in forecasting weather conditions. Statement 2: Statistical method of correlation helps only in forecasting weather conditions.
A. Both statements are true
B. Both statements are false
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Answer: C. Statement 1 is true, Statement 2 is false

Q29. A 95% confidence interval of sample mean can be calculated by:
A. Mean ± Standard deviation
B. Mean ± 1.96 × Standard error
C. Mean ± Variance
D. Mean ± 1.96 × σ/√n
Answer: B and D

Q30. Coefficient of variation is measured by:
A. Mean / Standard deviation × 100
B. Variance / Mean × 100
C. Standard deviation / Mean × 100
D. Mean / Variance × 100
Answer: C. Standard deviation / Mean × 100

Q31. Match the following correctly:
A. Standard deviation — Variation
B. Error — Constructing 95% confidence interval
C. Regression — Dependent and independent variables
D. Bonferroni method — Used after ANOVA
Answer: All are correctly matched

Q32. Which are properties of normal distribution?
A. It is bell-shaped
B. It is symmetrical
C. Mean ± 2σ covers about 95% observations
D. All of the above
Answer: D. All of the above

Q33. Which are correct examples of Type II error?
A. Not rejecting null hypothesis when it is actually false
B. Rejecting null hypothesis when it is actually true
C. A drug is actually effective but declared not effective
D. A drug is not effective but declared effective
Answer: A and C

Q34. Which of the following are parametric tests?
A. Chi-square test and McNemar test
B. t-test and F-test
C. Wilcoxon signed-rank test and Chi-square test
D. Mann-Whitney test and McNemar test
Answer: B. t-test and F-test

Q35. Which facts related to p-value are correct?
A. p-value is fixed
B. p-value is calculated from sample data
C. p-value is always greater than 1
D. For significant result, p-value should be less than the level of significance
Answer: B and D

Q36. To find the degree of linear relationship between age and height of a tree, we use:
A. Regression coefficient
B. Correlation coefficient
C. Standard deviation
D. Coefficient of variation
Answer: B. Correlation coefficient

Q37. Least square estimators have the smallest variance among all unbiased linear estimators. This belongs to:
A. Bayes theorem
B. Central limit theorem
C. Chebyshev theorem
D. Gauss-Markov theorem
Answer: D. Gauss-Markov theorem

Q38. Statement 1: Mean deviation is a better measure of dispersion than quartile deviation. Statement 2: Mean deviation takes the algebraic sum of deviations.
A. Both statements are true
B. Both statements are false
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Answer: C. Statement 1 is true, Statement 2 is false

Q39. Which statements are correct about lines of regression between X and Y?
A. Correlation coefficient is the geometric mean of regression coefficients
B. If two variables are uncorrelated, regression lines are perpendicular
C. If one regression coefficient is greater than 1, the other must also be greater than 1
D. All are correct
Answer: A and B

Q40. Probability that a standard normal variate lies between -∞ and +1 is approximately:
A. 0.84
B. 0.68
C. 0.50
D. 0.95
Answer: A. 0.84

Q41. Time clocked by an athlete in a 100-metre race is an example of:
A. Discrete variable
B. Continuous variable
C. Nominal variable
D. Ordinal variable
Answer: B. Continuous variable

Q42. Which statements are correct?
A. Arithmetic Mean is greater than Geometric Mean for two non-equal positive values
B. Correlation coefficient shows causal relationship
C. Regression coefficient is independent of origin
D. Regression coefficient is independent of scale
Answer: A and C

Q43. For a regression model, explained sum of squares is 75 and unexplained sum of squares is 25. Coefficient of determination is:
A. 0.25
B. 0.50
C. 0.60
D. 0.75
Answer: D. 0.75

Q44. In a class of 13 students, 3 students fail. Marks of passed students are arranged, and the median of the total class is asked. The median is:
A. 4
B. 5
C. 6
D. 7
Answer: C. 6

Q45. In one-way ANOVA with k treatments, the degree of freedom for mean error sum of squares is:
A. k - 1
B. N - 1
C. N + k
D. N - k
Answer: D. N - k

Q46. Which statements are correct regarding sampling theory?
A. Standard error is the standard deviation of sampling distribution
B. Standard error is inversely proportional to sample size
C. Type I error means accepting a wrong null hypothesis
D. Type II error means rejecting a true null hypothesis
Answer: A and B

Q47. If means of two groups with m and n observations are 40 and 60 respectively, and combined mean is 48, the ratio m:n is:
A. 2:3
B. 3:2
C. 4:3
D. 5:2
Answer: B. 3:2

Q48. Which statements are correct?
A. In positively skewed distribution, Mean > Median > Mode
B. In negatively skewed distribution, Mode > Median > Mean
C. Karl Pearson coefficient lies between ±1
D. Bowley coefficient lies between ±1
Answer: A, B and D

Q49. Which statement is correct regarding range as a measure of dispersion?
A. Range is dependent on origin and scale
B. Range is independent of origin but not of scale
C. Range is independent of both origin and scale
D. Range is dependent only on origin
Answer: B. Range is independent of origin but not of scale

Q50. Which statements are correct about normal distribution?
A. It is applicable to continuous random variables
B. It is symmetrical
C. All values are equally likely
D. Standard normal distribution has mean 0 and standard deviation 1
Answer: A, B and D

Q51. Assertion: Regression analysis is suitable for two variables where dependent and independent variables have a causal linear relationship. Reason: The causal relationship between two variables is never curvilinear.
A. Both Assertion and Reason are true, and Reason is correct explanation
B. Both Assertion and Reason are true, but Reason is not correct explanation
C. Assertion is true, but Reason is false
D. Assertion is false, but Reason is true
Answer: C. Assertion is true, but Reason is false

Q52. Match the following statistical tests with their uses:
A. Chi-square test — Goodness of fit
B. One-way ANOVA — Comparing means of more than two groups
C. Paired t-test — Difference between paired means
D. t-test — Testing a single mean
Answer: All are correctly matched

Q53. Statement 1: Covariance between two variables X and Y determines whether correlation is positive or negative. Statement 2: The product of standard deviations can be both positive and negative.
A. Both statements are true
B. Both statements are false
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Answer: C. Statement 1 is true, Statement 2 is false

Q54. Statement 1: Leslie matrix population model is a discrete and age-independent model. Statement 2: The first row in Leslie projection matrix represents fertility.
A. Both statements are true
B. Both statements are false
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Answer: D. Statement 1 is false, Statement 2 is true

Q55. In an objective-type examination, 100 questions are given. Each correct answer carries 1 mark and 0.2 mark is deducted for each incorrect answer. Since the number of questions is fixed, this is an example of:
A. Continuous variable
B. Nominal variable
C. Discrete variable
D. Ordinal variable
Answer: C. Discrete variable

Q56. A random variable X follows Poisson distribution such that P(X = 1) = P(X = 2). Which statements are correct?
A. λ = 2
B. Mean = 2
C. Variance = 2
D. Mean and variance are unequal
Answer: A, B and C

Q57. Given ΣX = 230, ΣX² = 6500 and n = 10, the standard deviation is:
A. 9
B. 10
C. 11
D. 12
Answer: C. 11

Q58. Gender is an example of:
A. Ordinal variable
B. Nominal variable
C. Continuous variable
D. Ratio variable
Answer: B. Nominal variable

Q59. If the number of questions and marks in an objective-type examination are fixed, the variable is:
A. Discrete variable
B. Continuous variable
C. Nominal variable
D. Interval variable
Answer: A. Discrete variable

Q60. The mean marks of 200 students is 47. The top 25% students have mean marks of 72, and the bottom 25% students have mean marks of 25. The mean marks of the remaining students is:
A. 40.5
B. 42.5
C. 45.5
D. 48.5
Answer: C. 45.5

Q61. If X is a random variable that follows normal distribution with mean μ and standard deviation σ, then Chi-square distribution with one degree of freedom is represented by:
A. (X - μ) / σ
B. [(X - μ)²] / σ²
C. (X + μ) / σ
D. σ² / (X - μ)²
Answer: B. [(X - μ)²] / σ²

Q62. Which statements are correct for Poisson distribution?
A. Mean is equal to variance
B. It is used for count data
C. It has parameter λ
D. All of the above
Answer: D. All of the above

Benefits of Practising UGC NET Environmental Science Unit 9 PYQs 

Practising UGC NET Environmental Science Unit 9 PYQs helps students prepare the Statistical Approaches section with better clarity. Since this unit includes many formulas, concepts, and numerical questions, PYQs make revision more exam-focused.

• Helps understand repeated concepts: PYQs show which topics are frequently asked, such as mean, variance, standard deviation, correlation, regression, ANOVA, and Chi-square test.

• Improves numerical accuracy: Unit 9 includes calculation-based questions. Regular practice helps students reduce mistakes and solve questions faster.

• Builds formula clarity: Solving PYQs helps students remember important formulas related to standard deviation, coefficient of variation, confidence interval, probability, and regression.

• Improves exam confidence: Previous year questions give students a clear idea of the question pattern and difficulty level.

• Supports quick revision: PYQs are useful for revising important topics in less time before the exam.

• Helps identify weak areas: Students can easily find the topics where they make repeated mistakes and revise them again.

• Makes preparation more focused: Instead of studying all topics randomly, PYQs help students focus on areas that are more important for the UGC NET Environmental Science exam.