Question bank

1. Define statistics.
2. Differentiate between population and sample.
3. What are the different sampling methods?
4. Explain simple random sampling
5. Explain stratified random sampling
6. Explain systematic sampling.
7. What are the different types of data? Explain with examples.
8. Explain different scales of measurement with examples.
9. What is a frequency distribution?
10. What is a variable?
11. What is frequency?
12. What are the different types of diagrams to represent data? Explain.
13. What are the different graphs used to represent frequency distributions?
14. Explain the method of locating mode graphically.
15. Explain the method of locating median graphically.
16. Write a short note on stem and leaf chart.
17. What are the requisites of a good measure of central tendency?
18. What is the formula to find AM for ungrouped and grouped data?
19. What are the properties of AM?
20. Prove any two properties of AM?
21. Write the merits and demerits of AM.
22. What is weighted AM? Write the formula to find it.
23. What is trimmed mean?
24. Derive an expression to find the combined mean of two groups.
25. What are the two measures of central tendecy that can be located graphically?
26. Write the formula to find median for ungrouped data.
27. Explain the procedure of finding median for discrete frequency distribution.
28. Explain the procedure of finding median for continuous frequency distribution.
29. Write the merits and demerits of median.
30. What is mode?
31. Write the formula to find out mode for continuous frequency distribution.
32. Write the merits and demerits of mode.
33. Define geometric mean. Write formula for grouped and ungrouped data.
34. Derive an expression for combined GM of two groups.
35. Define HM. Write its formula for grouped and ungrouped data.
36. Write the merits and demerits of GM.
37. Write the merits and demerits of HM.
38. Show that (GM)2 = (AM)(HM)
39. Show that AM≥GM≥HM
40. What are absolute and relative measures of dispersion?
41. What are the different measures of dispersion?
42. What is range and coefficient of range?
43. Write formula for Q.D and its coefficient.
44. Write the formula for mean deviation.
45. Write formula for standard deviation for grouped and ungrouped data.
46. Show that that standard deviation is not less than mean deviation from mean.
47. What is Gini”s coefficient?
48. Write a short note on Lorenz curve.
49. Differentiate between central and raw moments.
50. Derive an expression for central moments in terms of raw moments and vice
versa,
51. What are outliers?
52. Write a short note on box plot.
53. What is skewness? Explain with the help of a diagram
54. What are the measures of skewness?
55. Show that Bowley’s coefficient of skewness lies between -1 and +1
56. Explain the concept of kurtosis with the help of a diagram.
57. Explain scatter plot with the help of diagrams.
58. What is correlation?
59. Differentiate between positive and negative correlation.
60. Write and expression for Karl Person’s coefficient of correlation.
61. Write a short note on probable error.
62. What are the properties of Karl Person’s coefficient of correlation?
63. Show that Karl Pearson’s coefficient of correlation lies between -1 and +1.
64. Show that Karl Pearson’s coefficient of correlation is independent of change of
origin and scale.
65. Show that Karl Person’s coefficient of correlationis symmetric.
66. What is coefficient of determination?
67. Derive an expression for Spearman’s rank correlation coefficient.
68. Write the formula for Spearman’s rank correlation coefficient when there is tie
in ranking.
69. State the principle of least squares.
70. Explain the procedure of fitting of a straight line.
71. Explain the procedure of fitting of a second degree curve.
72. Explain the procedure of fitting the curve Y = axb
73. Explain the procedure of fitting the curve Y = abx
74. Explain the procedure of fitting the curve Y = aebx
75. Derive expression for regression coefficient byx
76. Write the properties of regression coefficients and prove any two of them.
77. Write the expression for Yule’s coefficient of association.
78. What is odds ratio?
79. Write short note on mean vector and dispersion matrix.
80. Differentiate between multiple and partial correlation.
81. Write an expresssion for the plane of regression in the case of trivariate data.
82. Write expression for b12.3 and b13.2
83. Write an expression for multiple correlation coefficient.
84. Write an expression for partial correlation coefficient.
85. Show that (1- R21.23) =(1-r 212)(1-r 213.2)