Mathematics-IV Unit 5 – Statistical Techniques III: AKTU previous year questions
47 AKTU questions from Unit 5 (Statistical Techniques III) asked in 2021–2026, tagged by marks, year and topic. In short: about 29 marks of every paper come from this unit; the most asked topic is Statistical Tests of Significance (22 times); 37 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 5 previous year questions
- What is a control chart? Name any two types of control charts. (2 marks, 2026, Statistical Quality Control)
- Two independent random samples from two normal populations gave the following results: Sample I: size 10, mean 52, SD 6; Sample II: size 12, mean 47, SD 5. Test whether the difference between the sample means is significant at 5% level of significance. Assume population variances are equal. (7 marks, 2026, Statistical Tests of Significance)
- The following table shows the distribution of students according to gender and preference of subject: Male: Science 50, Arts 30, Commerce 20, Total 100; Female: Science 40, Arts 50, Commerce 30, Total 120; Total: 90, 80, 50, 220. Test at 5% level of significance whether gender and subject preference are independent. (7 marks, 2026, Statistical Tests of Significance)
- Five samples, each of size 4, were taken from a production process. The sample means and ranges are given below: Sample 1: mean 20, R 4; Sample 2: mean 22, R 5; Sample 3: mean 19, R 3; Sample 4: mean 21, R 4; Sample 5: mean 23, R 6. Construct x̄-chart and R-chart and comment on whether the process is under control. Given A2 = 0.729, D3 = 0, D4 = 2.282. (7 marks, 2026, Statistical Quality Control)
- What do you mean by statistical quality control? (2 marks, 2025, Statistical Quality Control)
- Write the formula of Chi-square χ² test. (2 marks, 2025, Statistical Tests of Significance)
- Define the Null hypothesis. (2 marks, 2025, Sampling Theory and Hypothesis)
- The following table shows the distribution of digits in numbers chosen at random from a telephone directory: Digits 0-9, Frequency: 1026 1107 997 966 1075 933 1107 972 964 853. Test whether the digits may be taken to occur equally frequently in the directory. (χ² at 5% level of significance for 9 d.f. is 16.919). (7 marks, 2025, Statistical Tests of Significance)
- What are statistical quality control techniques? Discuss the objectives and advantages of SQC. (7 marks, 2025, Statistical Quality Control)
- The 9 items of a sample have the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean of these values differ significantly from the assumed mean 47.5? (t₀.₀₅ = 2.31 for γ = 8). (7 marks, 2025, Statistical Tests of Significance)
- Two independent samples of 8 and 7 items respectively had the following values of the variables: Sample I: 9 11 13 11 15 9 12 14, Sample II: 10 12 10 14 9 8 10. Is the difference between the means of the sample significant? (7 marks, 2025, Statistical Tests of Significance)
- In a blade manufacturing factory, 1000 blades are examined daily. Draw the np chart for the following table and examine whether the process is under control? Date 1-15, No. of Defective blades: 9 10 12 8 7 15 10 12 10 8 7 13 14 15 16. (7 marks, 2025, Statistical Quality Control)
Most asked Unit 5 topics
- Statistical Tests of Significance – asked 22 times
- Statistical Quality Control – asked 16 times
- Sampling Theory and Hypothesis – asked 9 times
Unit 5 question pattern
- 2-mark questions: 17 asked in 2021–2026
- 7-mark questions: 15 asked in 2021–2026
- 10-mark questions: 15 asked in 2021–2026
- About 29 marks from Unit 5 in every paper
- 37 questions were asked again in a later year
Unit 5 questions year by year
- 2026: 4 Unit 5 questions asked (23 marks across that year's papers)
- 2025: 9 Unit 5 questions asked (48 marks across that year's papers)
- 2024: 9 Unit 5 questions asked (48 marks across that year's papers)
- 2023: 10 Unit 5 questions asked (68 marks across that year's papers)
- 2022: 10 Unit 5 questions asked (68 marks across that year's papers)
- 2021: 5 Unit 5 questions asked (34 marks across that year's papers)