100+ Free Assam Higher Secondary Statistics Practice Questions

Prepare for the Assam State School Education Board (ASSEB/AHSEC) Higher Secondary (Class 11 & 12) Statistics Examination exam with instant access — no signup required.

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2026 Statistics

Key Facts: Assam Higher Secondary Statistics Exam

100

Total practice MCQs in this dedicated question bank

OpenExamPrep

30%

Minimum passing percentage for ASSEB HS exam

ASSEB Board Regulations

68.26%

Area under Normal curve within 1 standard deviation (μ ± 1σ)

Statistical Distribution Theory

NRR = 1

Indicator of exact female population replacement

Demographic & Vital Statistics Standards

3-Sigma

Standard Shewhart control limit distance for SQC charts

Statistical Quality Control Manual

Assam ASSEB Higher Secondary Statistics evaluates Class 11 and 12 students on probability distributions, statistical inference, time series trend calculations, index numbers, vital statistics mortality/fertility rates, and control charts.

Sample Assam Higher Secondary Statistics Practice Questions

Try these sample questions to test your Assam Higher Secondary Statistics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If two fair six-sided dice are rolled simultaneously, what is the probability of obtaining a sum equal to 8?

A.5/36

B.1/6

C.1/9

D.7/36

Explanation: The total number of outcomes when rolling two fair dice is 6 * 6 = 36. The favorable outcomes yielding a sum of 8 are (2,6), (3,5), (4,4), (5,3), and (6,2), which total 5 outcomes. Thus, P(Sum = 8) = 5/36.

2For two events A and B, if P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, what is the probability of P(A ∪ B)?

A.0.7

B.0.9

C.0.2

D.0.5

Explanation: By the addition theorem of probability, P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Substituting the given values: P(A ∪ B) = 0.4 + 0.5 - 0.2 = 0.7.

3Two events A and B are statistically independent. If P(A) = 0.3 and P(B) = 0.6, what is P(A ∩ B)?

A.0.18

B.0.90

C.0.30

D.0.50

Explanation: For independent events A and B, the joint probability of their simultaneous occurrence is P(A ∩ B) = P(A) * P(B). Therefore, P(A ∩ B) = 0.3 * 0.6 = 0.18.

4If P(B) = 0.5 and P(A ∩ B) = 0.15, what is the conditional probability P(A | B)?

A.0.30

B.0.075

C.0.65

D.0.35

Explanation: The conditional probability P(A | B) is defined as P(A ∩ B) / P(B). Substituting the given values gives P(A | B) = 0.15 / 0.5 = 0.30.

5A bag contains 5 red balls and 3 black balls. Two balls are drawn successively without replacement. What is the probability that both drawn balls are red?

A.5/14

B.25/64

C.15/56

D.5/28

Explanation: The total number of balls is 8. The probability of drawing a red ball first is 5/8. Without replacement, 4 red balls and 7 total balls remain, making the second probability 4/7. Thus, P(Both Red) = (5/8) * (4/7) = 20/56 = 5/14.

6According to Bayes' Theorem, if event A partitions the sample space into mutually exclusive events A1 and A2, how is P(A1 | B) expressed?

A.P(B | A1)P(A1) / [P(B | A1)P(A1) + P(B | A2)P(A2)]

B.P(A1 ∩ B) / P(A1)

C.P(B | A1) / P(B)

D.P(A1)P(A2) / P(B)

Explanation: Bayes' Theorem updates the prior probability of an event A1 given new evidence B. It states P(A1 | B) = P(B | A1)P(A1) / P(B), where by total probability P(B) = P(B | A1)P(A1) + P(B | A2)P(A2).

7A discrete random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3 respectively. What is the mathematical expectation E(X)?

A.2.1

B.2.0

C.1.8

D.2.3

Explanation: The expectation E(X) is calculated as Σ [x * P(X = x)] = (1 * 0.2) + (2 * 0.5) + (3 * 0.3) = 0.2 + 1.0 + 0.9 = 2.1.

8For a random variable X, if E(X) = 4 and E(X^2) = 25, what is the variance Var(X)?

A.9

B.21

C.16

D.5

Explanation: Variance of X is defined as Var(X) = E(X^2) - [E(X)]^2. Substituting the given values: Var(X) = 25 - (4)^2 = 25 - 16 = 9.

9If X and Y are independent random variables with Var(X) = 4 and Var(Y) = 5, what is Var(3X - 2Y)?

A.56

B.16

C.26

D.44

Explanation: For independent random variables, Var(aX + bY) = a^2 * Var(X) + b^2 * Var(Y). Here, a = 3 and b = -2. So, Var(3X - 2Y) = (3)^2 * Var(X) + (-2)^2 * Var(Y) = 9 * 4 + 4 * 5 = 36 + 20 = 56.

10If a random variable X has expectation E(X) = c, what is the value of E(X - c)?

A.0

B.c

C.c^2

D.1

Explanation: By properties of expectation, E(X - c) = E(X) - E(c) = E(X) - c. Since E(X) = c, E(X - c) = c - c = 0. The expected deviation from the mean is always zero.

About the Assam Higher Secondary Statistics Exam

The ASSEB HS Statistics curriculum equips Class 11 and 12 students with essential theoretical knowledge and practical numerical skills in statistics. Key areas include probability theory, discrete and continuous distributions (Binomial, Poisson, Normal), sampling techniques, estimation, hypothesis testing (Z-test, t-test, Chi-square test, F-test), time series component analysis and trend fitting, index number formulation and adequacy tests (Laspeyres, Paasche, Fisher, Time and Factor Reversal tests), demographic measures of mortality and fertility, life tables, and statistical process quality control.

Assessment

The ASSEB Higher Secondary Statistics examination consists of theoretical concepts, mathematical proofs, and numerical calculations across Probability, Statistical Inference, Time Series, Index Numbers, Vital Statistics, and Quality Control.

Time Limit

3 hours

Passing Score

30% aggregate

Exam Fee

Standard ASSEB board examination fee (Assam State School Education Board (ASSEB))

Assam Higher Secondary Statistics Exam Content Outline

15%

Unit 1: Probability Theory & Random Variables

Classical, empirical, and axiomatic probability, addition and multiplication theorems, conditional probability, Bayes' theorem, discrete/continuous random variables, expectation, variance, and MGF.

20%

Unit 2: Probability Distributions (Binomial, Poisson, Normal)

PMF/PDF formulas, mean and variance parameters, limiting forms, additive properties, standard normal transformation Z, empirical rule (68-95-99.7), and inflection points.

15%

Unit 3: Sampling Theory & Point Estimation

Census vs sample survey, sampling/non-sampling errors, simple random sampling (SRSWR/SRSWOR), stratified, systematic sampling, properties of estimators (unbiasedness, consistency, efficiency, sufficiency), and standard error.

20%

Unit 4: Hypothesis Testing & Small/Large Sample Tests

Null/alternative hypotheses, Type I and Type II errors, power of test, critical regions, Z-test for large samples, Student's t-test (single mean, paired samples), Chi-Square test (goodness of fit, r×c contingency tables), and F-test for variances.

12%

Unit 5: Time Series Analysis

Components of time series (T, S, C, I), additive and multiplicative models, measurement of trend via semi-averages, moving averages, and least squares method Y = a + bX.

10%

Unit 6: Index Numbers & Tests of Adequacy

Unweighted and weighted index numbers, Laspeyres, Paasche, Fisher's Ideal Index, Marshall-Edgeworth Index, Consumer Price Index (CPI), Time Reversal Test, and Factor Reversal Test.

Unit 7: Vital Statistics & Demography

Mortality rates (CDR, SDR, IMR, STDR), life tables (lx, dx, qx, ex°), fertility rates (CBR, GFR, ASFR, TFR), Gross Reproduction Rate (GRR), and Net Reproduction Rate (NRR).

Unit 8: Statistical Quality Control (SQC)

Chance vs assignable causes of variation, Shewhart 3-sigma control limits, control charts for variables (X-bar and R chart), and control charts for attributes (p, np, c, u charts).

How to Pass the Assam Higher Secondary Statistics Exam

What You Need to Know

Passing score: 30% aggregate
Assessment: The ASSEB Higher Secondary Statistics examination consists of theoretical concepts, mathematical proofs, and numerical calculations across Probability, Statistical Inference, Time Series, Index Numbers, Vital Statistics, and Quality Control.
Time limit: 3 hours
Exam fee: Standard ASSEB board examination fee

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Assam Higher Secondary Statistics Study Tips from Top Performers

1Master key distribution formulas: Binomial Mean = np, Var = npq; Poisson Mean = Var = λ; Normal Standard variate Z = (X - μ)/σ.

2Practice worked numerical calculations for least squares linear trend Y = a + bX, Fisher's index √(L * P), sample standard error s/√n, and Chi-Square goodness of fit ∑[(O - E)^2 / E].

3Memorize degrees of freedom formulas: Single mean t-test (n - 1), paired t-test (n - 1), Chi-Square r×c contingency table (r - 1)(c - 1).

4Understand time series decomposition: Additive (Y = T + S + C + I) vs Multiplicative (Y = T * S * C * I) models and moving average period properties.

5Study life table column relationships: d_x = l_x - l_{x+1}, q_x = d_x / l_x, p_x = 1 - q_x, e_x° = T_x / l_x.

6Differentiate between control charts for variables (X-bar and R chart) and control charts for attributes (p, np, c, u charts) in Statistical Quality Control.

Frequently Asked Questions

What topics are covered in the Assam ASSEB HS Statistics syllabus?

The Class 11 and 12 Higher Secondary Statistics syllabus covers Probability Theory, Random Variables & Expectations, Probability Distributions (Binomial, Poisson, Normal), Sampling Theory & Estimation, Hypothesis Testing (Z-test, Student's t-test, Chi-Square test, F-test), Time Series Analysis, Index Numbers (Laspeyres, Paasche, Fisher), Vital Statistics & Life Tables, and Statistical Quality Control (SQC).

What is the pass mark for ASSEB HS Statistics?

Students must secure a minimum of 30% marks overall to pass the Higher Secondary Statistics examination.

Why is Fisher's Index known as the Ideal Index Number?

Fisher's Index is geometric mean of Laspeyres and Paasche indices. It is called 'Ideal' because it incorporates both base and current year quantities as weights and uniquely satisfies both the Time Reversal Test (P01 * P10 = 1) and the Factor Reversal Test (P01 * Q01 = V01).

What is the difference between Type I and Type II errors in hypothesis testing?

A Type I Error occurs when a true null hypothesis (H0) is incorrectly rejected (probability α). A Type II Error occurs when a false null hypothesis is incorrectly accepted (probability β). The power of a test is 1 - β.

What are the key properties of the Normal Distribution?

The Normal distribution is continuous, symmetric, bell-shaped about mean μ where Mean = Median = Mode. Total area under pdf equals 1.0. Skewness β1 = 0, Kurtosis β2 = 3. Inflection points occur at μ ± σ. Approximately 68.26% of data lies within μ ± 1σ, 95.44% within μ ± 2σ, and 99.73% within μ ± 3σ.

What is the difference between GRR and NRR in Vital Statistics?

Gross Reproduction Rate (GRR) measures potential female population replacement assuming no female mortality before age 49. Net Reproduction Rate (NRR) accounts for female mortality using survival probabilities (l_x). Thus NRR ≤ GRR always. NRR = 1 indicates stable female population replacement.

100+ Free Assam Higher Secondary Statistics Practice Questions

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