Mathematics-IV Unit 3 Notes AKTU (BAS303)

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Unit 3 · Notes

AKTU Mathematics-IV (BAS303) Unit 3 notes for B.Tech Semester 3/4 – Statistical Techniques I. Topics: Measures of Central Tendency, Curve Fitting Least…

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Unit 3: Statistical Techniques I – AKTU syllabus topics

  • Measures of Central Tendency: Moments Skewness Kurtosis
  • Curve Fitting Least Squares: Fitting Straight Line Parabola, Fitting Exponential Curves
  • Correlation and Rank Correlation
  • Regression Analysis: Regression Line Y on X, Regression Line X on Y

Most asked AKTU PYQ questions from Unit 3

  1. Q5b. The following table gives age (x) in years of cars and annual maintenance cost (y) in hundred rupees. x: 1 3 5 7 9, y: 15 18 21 23 22. Calculate the maintenance cost for a 4-year-old car after finding the regression equation. (10 marks, 2020-21)
  2. Q5b. Calculate all four moments about mean and also skewness and kurtosis. Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70, Students: 1 6 10 15 11 7 10. (7 marks, 2024-25)
  3. Q5b. Determine the skewness and kurtosis for the following data: Marks: 10-20 20-30 30-40 40-50 50-60, No. of students: 18 20 30 22 10. (7 marks, 2023-24)
  4. Q5b. The first four moments of a distribution about the value 4 of the variables are -1.5, 17, -30 and 80. Find moments μ₁, μ₂, μ₃, μ₄ about mean. Also find β₁ and β₂. (10 marks, 2022-23)
  5. Q5a. Compute skewness and kurtosis, if the first four moments of a frequency distribution about the value 4 of the variable are 1, 4, 10 and 45. (10 marks, 2021-22)
  6. Q2c. From the following data, determine the equations of line of regression of y on x and x on y. x: 6 2 10 4 8, y: 9 11 5 8 7. (10 marks, 2021-22)
  7. Q2c. Calculate the first four central moments about the mean of the following data: x: 0 1 2 3 4 5 6 7 8, f: 1 8 28 56 70 56 28 8 1. (10 marks, 2021-22)
  8. Q5a. The following data give the frequency distribution of a variable X: X: 10 20 30 40 50, f: 3 7 12 8 4. Find the first four moments about the mean and hence determine the coefficients of skewness and kurtosis. (7 marks, 2025-26)
  9. Q5b. For 10 observations on price (x) and supply (y), the following data were obtained: Σx = 130, Σy = 220, Σx² = 2288, Σy² = 5506 and Σxy = 3467. Obtain the two lines of regression and estimate the supply when the price is 16 units. (7 marks, 2024-25)
  10. Q2c. The first four moments about the working mean 28.5 of a distribution are 0.294, 7.144, 42.409 and 454.98. Calculate the moments about the mean. Also evaluate β1, β2 and comment upon the skewness and kurtosis of the distribution. (7 marks, 2024-25)

AKTU paper codes: BAS303, BAS303H, BAS403, BAS403H, KAS302, KAS402

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