If you are preparing for your upcoming IGNOU exams and need accurate, stepwise solved answers for AST-01, you are in the right place. Unnati Education has prepared a complete AST-01 Statistical Techniques Solved Question Paper December 2025. This resource is built for BA, B.Com, and B.Sc students enrolled under the BDP programme.

About This Solved Paper

Field	Details
Prepared by	Unnati Education Team — IGNOU-experienced academic content writer
Qualification	Graduate with specialisation in Statistics and Mathematics
Course Name	Bachelor of Arts (BA), Bachelor of Commerce (B.Com), B.Sc (Application Oriented Courses)
Institution Reference	IGNOU Term-End Examination, December 2025

Download Now — Get AST-01 December 2025 Solved Question Paper

Do not waste time on incomplete Telegram files that skip steps or get formulas wrong. Unnati Education has the AST 1 Question Paper December 2025 solved paper ready with properly worked numerical solutions that match the actual December 2025 examination. Get it now and build real exam confidence.

Get AST-01 Solved Paper Now

What is AST-01 Question Paper December 2025?

The AST 01 December 2025 question paper is the official IGNOU Term-End Examination for Statistical Techniques under BDP, carrying 50 marks, with Q7 compulsory and any four questions from Q1 to Q6, completed in 2 hours without a calculator.

AST-01 is an Application Oriented Course under IGNOU's Bachelor's Degree Programme. Question 7 carries 10 marks through five true or false sub-parts requiring justification. Questions 1 to 6 each carry 10 marks covering numerical and conceptual problems. Students must attempt any four from these six. The paper tests a range of statistical methods from basic data handling through to hypothesis testing and quality control.

About IGNOU AST-01 — Statistical Techniques

AST-01 is a subject that teaches students how to collect, organise, analyse, and interpret data using standard statistical tools. You study descriptive statistics including mean and frequency distributions, probability distributions like Binomial and Poisson, sampling techniques, estimation, hypothesis testing through ANOVA and chi-square, correlation, and quality control using control charts.

Most students find probability and sampling the trickiest sections. That is because these require not just formula recall but understanding when to apply which method. Once you see a worked solution that explains the logic behind each step, these topics become far more manageable. Unnati Education's solved paper is written with that clarity in mind throughout.

AST-01 December 2025 — Question Paper Pattern and Marks Breakdown

50

Total Marks

2 hrs

Duration

10

Marks per Question

4+1

Attempt (4 optional + Q7)

Question 7 is fully compulsory and carries 10 marks across five sub-parts of 2 marks each. These test conceptual understanding through true or false statements with justification. From Questions 1 to 6, each carries 10 marks and you must attempt any four. Total marks are 50 and the exam runs for 2 hours. Here is the important part — calculators are not allowed, so all arithmetic must be done by hand. Choosing your four questions wisely based on topic strength is as important as knowing the methods themselves.

All Questions — AST-01 December 2025 Question Paper (Complete List)

IGNOU Term-End Examination — December 2025

Below are all questions exactly as set in the IGNOU December 2025 examination. Your solved paper covers stepwise answers for all of them.

1

Question 1

10 Marks

Part (a) 3 Marks

The table below shows the marks obtained by the students in a test:

Marks	Frequency
10	3
20	5
30	8
40	4
50	2

Find the mean of the given data.

Part (b) 2 Marks Data on the following variables were recorded for a study at a study centre in Delhi. Which of these are continuous and which are discrete?
(i) Age (ii) Year of birth (iii) Height (iv) Weight

Part (c) 5 Marks A factory produces steel rods of different lengths (in cm). The following are the lengths of 30 randomly selected rods:

102, 118, 125, 130, 135, 138, 140, 143, 147, 150, 152, 155, 160, 162, 165, 168, 170, 172, 175, 178, 180, 182, 185, 188, 190, 192, 195, 198, 200, 205

(i) Construct a frequency distribution using class intervals of width 20.
(ii) Draw a histogram based on frequency distribution.

2

Question 2

10 Marks

Part (a) 5 Marks A factory produces LED bulbs, and the probability that a randomly chosen bulb is defective, is 0.1. If a quality control inspector randomly selects 10 bulbs, what is the probability that:

(i) Exactly 2 bulbs are defective?
(ii) At most 2 bulbs are defective?

Part (b) 5 Marks The following table shows the annual profits (in Rs. lakhs) of a small business over a period of 6 years:

Year	Profit (Rs. lakhs)
2018	10
2019	12
2020	14
2021	16
2022	18
2023	20

(i) Calculate the 3-yearly moving average.
(ii) Plot original data and moving average obtained in part (i).

3

Question 3

10 Marks

Part (a) 6 Marks A teacher records the study hours and test scores (out of 10) for 5 students as follows:

Study Hours	Marks
2	3
3	4
5	5
7	6
8	7

Compute the correlation coefficient.

Part (b) 4 Marks A restaurant wants to estimate the average delivery time for its food orders. A random sample of 9 deliveries is recorded. It is obtained that the sample mean of delivery time is 20 minutes and standard deviation is 5 minutes. Find 95% confidence interval for the true average delivery time. (You may use the values given at the end of this question paper).

4

Question 4

10 Marks

Part (a) 7 Marks A company wants to compare customer's satisfaction across three different store locations. They collected satisfaction ratings (out of 10) from customers at each location, recorded as follows:

Store A	Store B	Store C
7, 8, 9, 6, 7	8, 9, 10, 7, 8	6, 7, 8, 6, 7

At a 5% significance level, perform a one-way ANOVA test to determine whether customers' satisfaction differs across store locations. (You may use the values given at the end of this question paper).

Part (b) 3 Marks Differentiate between simple random sampling with and without replacement.

5

Question 5

10 Marks

Part (a) 5 Marks A university has three departments with different number of students. The administration wants to conduct a survey by selecting a sample of 120 students using stratified random sampling. The total population and standard deviation in each department are given as follows:

Department	Science	Commerce	Arts
Total Students (Nᵢ)	500	300	200
SD (Sᵢ)	10	15	30

Find the sample size for each department using:
(i) Proportion allocation
(ii) Neyman allocation

Part (b) 5 Marks A teacher wants to estimate the average test score of 4 students, whose test scores are given as follows: 6, 4, 8, 2

(i) Calculate population mean.
(ii) Draw all possible samples of size 2 without replacement and calculate mean of each sample.
(iii) Show that sample mean is an unbiased estimate of the population mean.

6

Question 6

10 Marks

Part (a) 7 Marks For the following data, construct the X-bar control chart:

S. N.	X̄	R
1	19	4
2	20	5
3	21	3
4	20	4
5	19	5
6	22	4
7	20	3
8	21	5
9	20	4
10	18	3

Also interpret whether the process is under statistical control or not (Given A₂ = 0.577).

Part (b) 3 Marks A bag contains 5 red and 3 blue balls. A ball is drawn randomly, its colour is noted, and then it is placed back into the bag. This process is repeated twice. What is the probability that both balls drawn are red?

7

Question 7 — Compulsory

10 Marks · 5×2

Which of the following statements are True and which are False? Justify your answer. 5×2=10

Part (i) 2 MarksThe mean and variance of a Poisson distribution are 3 and 5 respectively.

Part (ii) 2 MarksProbability of accepting a lot of bad quality is called producer's risk.

Part (iii) 2 MarksThe value of every observation in the data set is taken into account when we calculate its median.

Part (iv) 2 MarksThe correlation coefficient lies between -1 and 1 (both limits included).

Part (v) 2 MarksThe Chi-square test is used for testing population mean.

Some Values for Use (if required)

Type	Values
Z-Values	Z₀.₉₅ = 1.96 \| Z₀.₉₀ = 2.33 \| Z₀.₉₉ = 1.645
F-Values	F₂,₁₂,(0.05) = 3.885 \| F₂,₁₃,(0.05) = 3.806 \| F₃,₁₂,(0.05) = 3.49
t-Values	t₉,₀.₀₂₅ = 2.262 \| t₈,₀.₀₂₅ = 2.306 \| t₉,₀.₀₅ = 1.833

AST-01 Syllabus Topics Covered in IGNOU December 2025 Question Paper

The December 2025 paper covers the complete AST-01 syllabus. Descriptive statistics including mean and frequency distribution appear in Q1. Probability distributions, specifically binomial, are tested in Q2 alongside time series through moving averages. Correlation and confidence interval estimation feature in Q3. One-way ANOVA and sampling theory run through Q4 and Q5. Stratified sampling with proportion and Neyman allocation is tested in Q5. Quality control through X-bar control charts appears in Q6. Q7 covers conceptual topics including Poisson distribution, producer's risk, median properties, correlation range, and chi-square test purpose.

Descriptive Statistics (Q1) Binomial Probability (Q2) Moving Averages (Q2) Correlation Coefficient (Q3) Confidence Intervals (Q3) One-Way ANOVA (Q4) Stratified Sampling (Q5) Neyman Allocation (Q5) X-bar Control Charts (Q6) Poisson Distribution (Q7) Chi-Square Test (Q7) Producer's / Consumer's Risk (Q7)

Sample Answer Preview — See How We Solve AST-01 Questions

Here is a brief preview of how our solved paper approaches Q1(a):

Given data: Marks 10, 20, 30, 40, 50 with frequencies 3, 5, 8, 4, 2.

Step 1: Total frequency = 3 + 5 + 8 + 4 + 2 = 22

Step 2: Sum of (marks × frequency) = (10×3) + (20×5) + (30×8) + (40×4) + (50×2) = 30 + 100 + 240 + 160 + 100 = 630

Step 3: Mean = 630 ÷ 22 = 28.64 approximately

Want complete stepwise solutions like this for every question in the paper? Get the full solved paper now.

Download Complete Solved Paper

How to Write High-Scoring Answers in AST-01 — Exam Tips

1

Always write the formula before substituting values. Examiners award method marks even if the final numerical answer has a small error, but only if the formula is correctly stated.

2

For true or false questions in Q7, never just write the verdict — your justification carries more weight than the label itself.

3

For ANOVA, always construct the full ANOVA table showing sum of squares, degrees of freedom, mean squares, and the F ratio.

4

For control chart questions, calculate the centre line and control limits clearly before plotting. Show all intermediate working.

5

In a no-calculator paper, neat and organised arithmetic is what separates good marks from average ones.

Who Should Use This AST-01 December 2025 Solved Question Paper?

BA, B.Com, and B.Sc students registered in the IGNOU BDP programme who are preparing for AST-01 in upcoming examinations.

Students who appeared in December 2025 and want to check their working will benefit equally.

Those preparing for competitive exams or postgraduate programmes that require statistical knowledge will also find the worked solutions useful as a structured reference beyond IGNOU preparation alone.

Why This Is Better Than Free AST-01 PDFs and Telegram Files

❌ Free Telegram Files

Wrong formulas and skipped steps
Solutions that do not match the actual December 2025 questions
One wrong step leads to completely wrong answers
Can actively damage your preparation
No quality check or accuracy guarantee

✔ Unnati Education

Prepared specifically for the December 2025 question paper
Correct formulas and accurate numerical working
Proper interpretation for every question
No shortcuts and no guesswork in any solution
Written by IGNOU-experienced academic content writers

Free AST-01 files on Telegram frequently contain wrong formulas, skipped steps, or solutions that do not match the actual December 2025 questions. In statistics, one wrong step leads to a completely wrong answer, which means a free PDF with errors can actively damage your preparation. Unnati Education's solved paper is prepared specifically for the December 2025 question paper with correct formulas, accurate numerical working, and proper interpretation for every question. There are no shortcuts and no guesswork in any solution.

Student Reviews — AST-01 Solved Paper by Unnati Education

★★★★★

The ANOVA and correlation solutions were completely stepwise. I finally understood how to set up the table correctly. Cleared AST-01 in December 2025 with good marks.

Amit Sharma — B.Sc IGNOU Delhi

★★★★★

The control chart construction and the binomial probability working were both very clear. Got the paper on WhatsApp quickly and it covered every question properly.

Neha Verma — B.Com IGNOU Jaipur

★★★★★

The stratified sampling and true or false justifications in Q7 were exactly what I needed. Very accurate and well explained throughout the paper.

Rohit Gupta — BA IGNOU Patna

How to Get the AST-01 December 2025 Solved Paper — Step by Step

1

Step 1: Contact Unnati Education through the WhatsApp number or order button on this page.

2

Step 2: Share your course code (AST-01) and confirm you need the December 2025 solved paper.

3

Step 3: Receive your complete solved paper instantly on WhatsApp or email. Fast, simple, and reliable.

Order on WhatsApp Now

Frequently Asked Questions — AST-01 December 2025

Q

What is AST-01 in IGNOU?

AST-01 is Statistical Techniques, an Application Oriented Course under IGNOU's Bachelor's Degree Programme. It covers descriptive statistics, probability distributions, sampling methods, estimation, hypothesis testing through ANOVA and chi-square tests, correlation analysis, and statistical quality control using control charts. The course is offered to BA, B.Com, and B.Sc students as part of the BDP curriculum.

Q

Which question is compulsory in AST-01 December 2025?

Question 7 is the compulsory question in the AST-01 December 2025 paper. It carries 10 marks and consists of five true or false statements that must be justified with reasoning. Each sub-part carries 2 marks. The remaining questions numbered 1 to 6 are optional and students must attempt any four. Each of those questions carries 10 marks, bringing the total to 50 marks.

Q

Is a calculator allowed in the AST-01 exam?

No, the use of a calculator is not allowed in the AST-01 December 2025 examination. All numerical calculations including mean, correlation, ANOVA, and probability must be worked out by hand within the 2-hour time limit. This makes it important to practise all calculations manually before the exam so that working speed and accuracy are both at a level that fits comfortably within the available time.

Q

What topics are most important for AST-01?

Based on the December 2025 paper, high-priority topics include mean and frequency distributions, binomial probability, moving averages, correlation coefficient, confidence intervals, one-way ANOVA, stratified sampling with proportion and Neyman allocation, X-bar control charts, and the conceptual properties of Poisson distribution, median, chi-square tests, and correlation range. These topics cover the complete question range in the December 2025 paper.

Q

What is the difference between producer's risk and consumer's risk in AST-01?

Producer's risk is the probability of rejecting a good quality lot, meaning the producer loses even though the product is acceptable. Consumer's risk is the probability of accepting a bad quality lot, meaning the consumer receives defective goods. In the December 2025 paper, Q7(ii) specifically tests whether students can correctly identify which risk corresponds to accepting a lot of bad quality, and the correct answer is consumer's risk, not producer's risk.

About Unnati Education — IGNOU Study Material Experts

Unnati Education has supported IGNOU students across India for several years, working exclusively on IGNOU academic resources including solved papers, assignments, guess papers, and subject notes. Every solved paper is prepared fresh for the specific examination cycle by writers who understand IGNOU's marking patterns and question styles. Students from hundreds of IGNOU centres across the country rely on our material because it is accurate, well-structured, and genuinely built for exam success. We do not recycle content or compromise on quality at any point.

Explore More IGNOU AST Solved Papers and Study Material

Unnati Education also provides assignment solutions for the current session, guess papers for upcoming examinations, and admission guidance for new IGNOU students. Browse our full range of BDP resources and Application Oriented Course materials to find everything you need for your upcoming exam preparation without searching across multiple platforms.

IGNOU Assignment Solutions IGNOU Guess Papers December 2025 IGNOU BDP Solved Papers IGNOU Admission Help

Get Your AST-01 December 2025 Solved Paper Now

You have the question paper right here. Now get the complete stepwise solutions with correct formulas, clear working, and proper interpretations that will help you prepare thoroughly for your upcoming IGNOU examination. Unnati Education's AST 1 Question Paper December 2025 solved paper is ready for immediate delivery. Contact us now and get it straight to your phone.

Get AST-01 Solved Paper on WhatsApp

Operations Research