| 5. | (a) | State, with reasons in brief, whether the following statements are true or false : | | |
| | | (i) | A single fact, even though numerically expressed cannot be called statistics. | | (0) |
| | | (ii) | It is safe to take the published statistics at their face value without knowing their meaning and limitations. | | (0) |
| | | (iii) | Median is a positional average. | | (0) |
| | | (iv) | A relative measure of dispersion cannot be used to compare dispersions of two or more distributions. | | (0) |
| | | (v) | The purpose of forecasting is to provide future data with perfect precision. | | (0) |
| | (2 marks each) | | |
| | (b) | Write the most appropriate answer from the given options in respect of the following: | | |
| | | (i) | The most acceptable and comprehensive definition of statistics in the sense of numerical data is given by – | (a) | Bowley | | (b) | Fisher | | (c) | Horace Secrist | | (d) | A.K. Sen. | | | (0) |
| | | (ii) | Which of the following statistical techniques is useful for economic planning – | (a) | Time series analysis | | (b) | Index numbers | | (c) | Forecasting techniques | | (d) | All of the above. | | | (0) |
| | | (iii) | Which of the following statements is not true about census investigation – | (a) | It is comprehensive | | (b) | More time is required | | (c) | Accuracy is very low | | (d) | Cost is very high. | | | (0) |
| | | (iv) | Which of the following is a mathematical average – | (a) | Median | | (b) | Mode | | (c) | Quartiles | | (d) | Harmonic mean. | | | (0) |
| | | (v) | Which of the following measures is suitable to study inequality of income and wealth– | (a) | Inter–quartile range | | (b) | Mean deviation | | (c) | Range | | (d) | Lorenz curve. | | | (0) |
| | | (vi) | The value of correlation coefficient ‘r’ is independent of – | (a) | Point of origin | | (b) | Unit of measurement | | (c) | Both (a) and (b) | | (d) | Neither (a) nor (b). | | | (0) |
| | | (vii) | Secular trend is the tendency of data to – | (a) | Increase over a long period of time | | (b) | Decrease over a long period of time | | (c) | Stagnate over a long period of time | | (d) | Either (a) or (b) or (c). | | | (0) |
| | | (viii) | Fisher’s ideal index number satisfies – | (a) | Unit test | | (b) | Time reversal test | | (c) | Factor reversal test | | (d) | All of the above. | | | (0) |
| | | (ix) | Tabulation of data is done – | (a) | Before classification | | (b) | After classification | | (c) | No restrictions | | (d) | None of the above. | | | (0) |
| | | (x) | Which of the following measures of central tendency can be used for further algebraic treatment – | (a) | Geometric mean | | (b) | Harmonic mean | | (c) | Arithmetic mean | | (d) | All of the above. | | | (0) |
| | (1 mark each) | | |
| 6. | (a) | Distinguish between any three of the following: | | |
| | | (i) | ‘Continuous variable’ and ‘discrete variable’. | | (0) |
| | | (ii) | ‘Exclusive series’ and ‘inclusive series’. | | (0) |
| | | (iii) | ‘Frequency polygon’ and ‘frequency curve’. | | (0) |
| | | (iv) | ‘Coefficient of variation’ and ‘variance’. | | (0) |
| | (3 marks each) | | |
| | (b) | Re–write the following sentences after filling–in the blank spaces with appropriate word(s)/figure(s) : | | |
| | | (i) | Arrangement of data on the basis of certain characteristics is called ___________of data. | | (0) |
| | | (ii) | In a statistical enquiry, ____________ is a person who answers to the set of questions included in the questionnaire. | | (0) |
| | | (iii) | In random sampling, each and every item of universe has ____________ probability of being selected. | | (0) |
| | | (iv) | ____________measures the degree and intensity of relationship between two variables. | | (0) |
| | | (v) | Data which have been collected by somebody else are called________________. | | (0) |
| | | (vi) | A diagram having two dimensions is known as______________. | | (0) |
| | (1 mark each) | | |
| 7. | Attempt any three of the following : | | |
| | (i) | Briefly explain the various stages of statistical enquiry. | | (0) |
| | (5 marks) | | |
| | (ii) | Differentiate between ‘census investigation’ and ‘sample investigation’. State the conditions in which census investigation is suitable. | | (0) |
| | (5 marks) | | |
| | (iii) | Define ‘average’. What are the characteristics of a good average ? | | (0) |
| | (5 marks) | | |
| | (iv) | Present the following data in the form of histogram on a graph sheet : Weekly Wages (Rs.) | No. of Workers | 10–15 15–20 20–25 25–30 30–40 40–60 60–80 | 7 10 27 15 12 12 8 | | | (0) |
| | (5 marks) | | |
| 8. | (a) | Calculate the mode from the following distribution | Wages more than (Rs.)No. of Workers | 80160 | 90151 | 100134 | 110104 | 12060 | 13029 | 14010 | | | (0) |
| | (5 marks) | | |
| | (b) | Calculate coefficient of standard deviation from the following data : | Marks ObtainedNo. of Students | 0–912 | 10–1915 | 20–2940 | 30–3922 | 40–491 | | | (0) |
| | (5 marks) | | |
| | (c) | From the information given below, find out the coefficient of correlation : No. of pairs of observation Assumed mean for X series Assumed mean for Y series Sum of deviations of X from assumed mean Sum of deviations of Y from assumed mean Sum of the multiplication of deviations of X and Y Total of square of deviations of X Total of square of deviations of Y | 10 82 68 (−) 170 (−) 20 3,044 8,288 2,264 | | | (0) |
| | (5 marks) | | |