Karnataka 2nd PUC Statistics Annual Exam Question Paper 2026 with Model Answers PDF
Karnataka 2nd PUC Statistics Annual Exam Question Paper 2026 with Model Answers PDF: Students can download the Karnataka 2nd PUC Statistics Annual Examination 2026 question paper along with its corresponding Model Answers. These resources help students understand the examination pattern, practise statistical calculations, improve problem-solving skills and prepare for future examinations.
The 2026 II PUC Annual Examination (Exam-1) Statistics paper carries 80 marks, contains 38 numbered questions and has a duration of three hours. The examination was scheduled for 2 March 2026, from 10:00 AM to 1:00 PM. The question paper contains Kannada and English versions, while the separate four-page Model Answers document provides solutions and marking guidance.
Karnataka 2nd PUC Statistics Annual Exam 2026 – Overview
| Particulars | Details |
|---|---|
| Board | Karnataka School Examination and Assessment Board (KSEAB) |
| Examination | Karnataka 2nd PUC (Class 12) |
| Examination Type | 2026 Annual Examination (Exam-1) |
| Subject | Statistics (ಸಂಖ್ಯಾಶಾಸ್ತ್ರ) |
| Subject Code | 31 (NS) |
| Exam Date | 2 March 2026 (Monday) |
| Exam Time | 10:00 AM to 1:00 PM |
| Maximum Marks | 80 |
| Duration | 3 Hours |
| Total Numbered Questions | 38 |
| Main Sections | A, B, C and D; Section E contains an accessibility alternative |
| Question Paper Language | Kannada and English |
| Model Answers Language | English |
| Question Paper Pages | 21 |
| Model Answers Pages | 4 |
| Document Format |
Download Statistics Annual Exam Question Paper 2026 with Model Answers PDF
Students can download the Karnataka 2nd PUC Statistics Annual Examination 2026 Question Paper and the corresponding Model Answers using the following separate PDF links.
| Document | Download PDF |
|---|---|
| Statistics Annual Question Paper 2026 21 Pages | 80 Marks | Exam-1 |
Download Question Paper |
| Statistics Annual Model Answers 2026 Model Answers | 4 Pages |
Download Model Answers |
Download Note: These Google Drive links open PDF copies supplied for educational use. If the documents open in preview mode, use the download option to save them for offline study.
Karnataka 2nd PUC Statistics Annual Exam 2026 Question Paper Pattern
The Statistics Annual Examination 2026 contains questions on vital statistics, index numbers, time series, probability distributions, statistical inference, hypothesis testing, statistical quality control, operations research and related numerical methods.
The regular paper has four main sections carrying a total of 80 marks.
| Section | Question Pattern | Marks |
|---|---|---|
| A | Multiple-choice, fill-in-the-blanks, matching and one-mark answers (Q1–Q16) | 20 |
| B | Answer any five short questions, 2 marks each (Q17–Q24) | 10 |
| C | Two groups of five-mark numerical questions (Q25–Q35) | 30 |
| D | Answer any two ten-mark questions (Q36–Q38) | 20 |
| Total | 80 | |
Section E: A separate alternative to the graph-based Question 35 is included for visually challenged students. It replaces the relevant question where applicable and is not an additional marks section.
Detailed Statistics Question-Wise Marks Distribution
| Question Numbers | Question Type and Choice | Marks |
|---|---|---|
| 1–5 | Five multiple-choice questions (5 × 1) | 5 |
| 6–10 | Five fill-in-the-blanks (5 × 1) | 5 |
| 11 | Five matching items (5 × 1) | 5 |
| 12–16 | Five one-mark questions (5 × 1) | 5 |
| 17–24 | Answer any five (5 × 2) | 10 |
| 25–31 | Answer any four numerical questions (4 × 5) | 20 |
| 32–35 | Answer any two numerical questions (2 × 5) | 10 |
| 36–38 | Answer any two long numerical questions (2 × 10) | 20 |
| Total | 80 | |
Important Instructions for Statistics Students
The original examination paper gives the following instructions:
- Statistical tables and graph sheets will be supplied on request.
- Scientific calculators are allowed.
- All working steps must be shown clearly.
- For Section A, only the first written answers will be considered for evaluation.
- An alternative to the graph question is provided for visually challenged students.
Students should follow the instructions printed in the applicable question paper and any updated examination directions issued by KSEAB.
Section A – Statistics Objective Questions
Section A carries 20 marks and tests basic statistical concepts and terminology.
The 2026 examination includes questions on:
- Vital Statistics: Fertility and fecundity.
- Index Numbers: Price-index changes and the base-year index.
- Probability Distributions: Mean of a t-distribution, Bernoulli distribution and standard error of a sample proportion.
- Operations Research: Fair games and the value of a game.
- Statistical Inference: Parameters, point estimation and significance level.
- Quality Control: Defective items.
- Replacement Problems: Minimum annual average cost.
- Linear Programming: Non-negativity restrictions.
Students should revise formulas, definitions and statistical notation before attempting the objective section.
Section B – Two-Mark Statistics Questions
Section B contains eight questions, numbered 17 to 24. Students must answer any five questions for ten marks.
| Question | Topic |
|---|---|
| 17 | Four stages of a business cycle. |
| 18 | Conditions for the binomial expansion method of interpolation and extrapolation. |
| 19 | Mean and variance of a Bernoulli distribution. |
| 20 | Features of the Poisson distribution. |
| 21 | Type-I and Type-II errors. |
| 22 | Calculation of a paired t-test statistic. |
| 23 | Causes of variation in a manufacturing process. |
| 24 | Calculation of economic order quantity. |
The Model Answers document gives the four business-cycle stages as prosperity, recession, depression and recovery. It also distinguishes Type-I and Type-II errors and identifies chance causes and assignable causes in quality control.
For numerical questions, students should write the formula, substitute the supplied values and show the final result with appropriate units.
Section C – Five-Mark Numerical Questions
Section C carries 30 marks and is divided into two groups. Questions 25–31 require any four answers, while Questions 32–35 require any two answers.
Questions 25–31 – Four Questions for 20 Marks
| Question | Numerical Problem |
|---|---|
| 25 | Calculate the Consumer Price Index by the aggregative expenditure method. |
| 26 | Interpolation and extrapolation of profit using the binomial expansion method. |
| 27 | Binomial probability involving three arrows aimed at a tree. |
| 28 | Hypergeometric distribution involving the selection of ripe mangoes. |
| 29 | Hypothesis testing of the standard deviation of wheat production. |
| 30 | Transportation problem using the North-West Corner Rule. |
| 31 | Optimum replacement period of a machine. |
These questions require students to choose the correct statistical method, prepare the relevant calculations and state the final conclusion.
Questions 32–35 – Two Questions for 10 Marks
- Question 32: Calculate probabilities from the normal distribution using weekly wage data.
- Question 33: Test whether the means of two samples differ significantly at the 1% significance level.
- Question 34: Find control limits for the number of defects per square metre.
- Question 35: Solve a linear programming problem graphically.
Students should practise drawing accurate graphs where required, checking feasible regions, identifying appropriate statistical tests and interpreting results.
Selected Numerical Results from the 2026 Statistics Model Answers
The accompanying four-page Model Answers document provides worked calculations and numerical results. Some examples are listed below to help students check their completed practice work.
| Question | Topic | Answer Reference |
|---|---|---|
| 24 | Economic Order Quantity | 1,000 units |
| 25 | Consumer Price Index | 147.64 |
| 26 | Interpolated and extrapolated profit | 2019: ₹17; 2025: ₹48 |
| 28 | Mean and variance | Mean = 1.8; Variance = 0.56 |
| 30 | Transportation Cost | ₹21,200 |
| 31 | Optimum Machine Replacement | End of the 4th year |
| 34 | Control Limits | LCL = 0, CL = 4, UCL = 10 |
| 35 | Linear Programming | x = 0, y = 600; Maximum Z = 1,800 |
Important: Students should not memorise only the final answers. The Scheme of Evaluation allocates marks to intermediate calculations, formulas, working tables and conclusions.
Section D – Ten-Mark Statistics Questions
Section D carries 20 marks. Students must answer any two questions from Questions 36 to 38.
Question 36 – Standardised Death Rates
Question 36 provides population and death figures for Village A and Village B across four age groups, along with a standard population.
Students must calculate the standardised death rates and determine which village is comparatively healthier based on the given data.
According to the Model Answers:
- Standardised Death Rate for Village A: 15.
- Standardised Death Rate for Village B: 14.
- Village B has the lower standardised death rate and is identified as comparatively healthier in this problem.
Question 37 – Fisher's Index Number
Question 37 requires students to show that Fisher's Index Number satisfies both the Time Reversal Test and Factor Reversal Test using the supplied price and quantity data.
For this question, students should:
- Prepare the necessary price and quantity product columns.
- Calculate the required aggregate values.
- Apply Fisher's index-number formula.
- Verify the time reversal test.
- Verify the factor reversal test.
The Model Answers provide the calculation framework and allocate marks to the relevant aggregates and test verification.
Question 38 – Time Series Analysis
Question 38 has two parts:
- Part (a): Calculate trend values using three-year moving averages.
- Part (b): Fit a linear trend using the method of least squares.
The Model Answers provide the final linear trend equation as Y = 18 + 0.2x, using the coded time values shown in the evaluation scheme.
Editorial Clarification: The supplied Model Answers appear to contain a transcription or arithmetic error in Question 38(b), showing the sum of the production values as 630. The six values printed in the question paper add to 108. The reported final trend equation Y = 18 + 0.2x is consistent with the question-paper data. The source PDF itself has not been altered.
Accessibility Alternative for Visually Challenged Students
The 2026 Statistics question paper provides a separate Section E for visually challenged students.
It contains an alternative to the graph-based Question 35, asking students to explain the steps involved in solving a Linear Programming Problem using the graphical method.
This is a five-mark alternative question, not an additional question to be answered by every candidate.
Students should follow the instructions applicable to their examination arrangements and refer to KSEAB for official accessibility provisions.
What Is Included in the Statistics Model Answers 2026?
The four-page Statistics Model Answers document provides solutions and marks allocation for the 2026 Annual Examination.
It includes:
- Correct multiple-choice and fill-in-the-blank responses.
- Matching answers and one-mark definitions.
- Formulas and answers for two-mark numerical problems.
- Consumer Price Index calculations.
- Interpolation and extrapolation solutions.
- Probability and distribution calculations.
- Hypothesis-testing calculations.
- Transportation problem allocations and cost.
- Replacement-period calculations.
- Control limits and Linear Programming solutions.
- Standardised death rates, index-number tests and time-series trend calculations.
Students should compare their complete working with the Model Answers. Final numerical results alone may not be sufficient to earn all allotted marks.
How to Practise the 2026 Statistics Annual Exam Question Paper
- Download the complete 21-page Statistics Annual Exam Question Paper 2026.
- Read the instructions and identify the internal choices in each section.
- Revise the formulas for probability distributions, index numbers and hypothesis testing.
- Attempt the objective questions without referring to the answer key.
- Practise two-mark definitions and shorter numerical problems.
- Prepare the required statistical tables before beginning longer calculations.
- Practise transportation problems, replacement decisions and Linear Programming.
- Revise ten-mark questions on standardised rates, index numbers and time series.
- Complete the paper within the prescribed three-hour duration.
- Compare calculations with the Model Answers and revise mistakes.
Study Tip: Always display formulas, substitutions, tables and final conclusions clearly. Accuracy of the method is important even when the final result is incorrect because of a calculation error.
Frequently Asked Questions
What is the subject code for Karnataka 2nd PUC Statistics?
The subject code printed on the 2026 Annual Examination question paper is 31 (NS).
How many questions are there in the Statistics Annual Exam 2026?
The question paper contains 38 numbered questions, with internal choices and a separate accessibility alternative.
What are the maximum marks and examination duration?
The Statistics examination carries 80 marks and has a duration of three hours.
Is the 2026 Statistics question paper bilingual?
Yes. The question paper contains Kannada and English versions.
Are scientific calculators allowed?
Yes. The supplied 2026 question paper explicitly states that scientific calculators are allowed. Students should also follow any applicable updated board instructions.
Are Statistics Model Answers available for 2026?
Yes. The corresponding four-page Model Answers document is available through the download table above.
Is this the Statistics Model Question Paper 2026–27?
No. This article provides the question paper and Model Answers from the 2026 Annual Examination (Exam-1). The 2026–27 model question papers are separate practice resources.
More Karnataka 2nd PUC Practice Papers
Students can also download the Karnataka 2nd PUC Statistics Model Question Papers 2026–27 – MQP 1 to 5.
For other subjects, visit the Karnataka 2nd PUC Model Question Papers 2027 – All Subjects collection.
Students can also practise the Psychology Annual Exam Question Paper 2026 with Model Answers.
For additional practice, visit the Economics Annual Exam Question Paper 2026 with Model Answers.
Students can also download the Geography Annual Exam Question Paper 2026 with Model Answers.
Official KSEAB Examination Information
For official examination announcements, question papers, model answers, timetables and notifications, students should refer to the Karnataka School Examination and Assessment Board.
Visit the Official KSEAB Website
Students should refer to KSEAB's original documents for authoritative examination instructions and current updates.
Source Note: The subject details, question pattern, marks distribution and numerical topics are based on the supplied KSEAB Statistics Annual Examination 2026 Question Paper and Model Answers. The examination date follows the KSEAB-issued 2026 Exam-1 final timetable. The PDF download links are Google Drive copies supplied for this article.
Disclaimer: PediaWikiBlog is an independent educational information website and is not affiliated with the Karnataka School Examination and Assessment Board (KSEAB). This article is provided for educational and examination-preparation purposes. Students should consult the official KSEAB website for examination instructions, updates and corrections.
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