5. | (a) | State, with reasons in brief, whether the following statements are true or false : | | |
| | (i) | Statistics can prove anything. | | (0) |
| | (ii) | It is essential to set the series into ascending or descending order to calculate mean. | | (0) |
| | (iii) | A distribution with greater co–efficient of variation is said to be more uniform. | | (0) |
| | (iv) | Karl Pearson's co–efficient of correlation is not suitable for use when dealing with qualitative characteristics. | | (0) |
| | (v) | Fisher’s index number is an ‘ideal index number’. | | (0) |
| (2 marks each) | | |
| (b) | Write the most appropriate answer from the given options in respect of the following: | | |
| | (i) | "Statistics is a science of estimates and probabilities." This definition is given by– (a) | Webster | (b) | Boddington | (c) | Selligman | (d) | Cowden. | | | (0) |
| | (ii) | Which of the following is not secondary data– (a) | Data published in research journals | (b) | Data published by WTO | (c) | Data published in news paper | (d) | Data obtained by a firm in a market survey. | | | (0) |
| | (iii) | When both lower and upper limits are considered, such classes are called – (a) | Exclusive | (b) | Inclusive | (c) | Cumulative | (d) | Mutually dependent | | | (0) |
| | (iv) | Which average is suitable to study the average intelligence level – (a) | Mode | (b) | Median | (c) | Arithmetic mean | (d) | Geometric mean. | | | (0) |
| | (v) | Which of the following can also be determined by graphic method–: (a) | Arithmetic mean | (b) | Harmonic mean | (c) | Geometric mean | (d) | Median. | | | (0) |
| | (vi) | The measure of variation that is least affected by extreme observations is – (a) | Range | (b) | Mean deviation | (c) | Standard deviation | (d) | Quartile deviation. | | | (0) |
| | (vii) | A distribution is called symmetrical when – (a) | X > Z | (b) | Z > X | (c) | M > X | (d) | X = M = Z. | | | (0) |
| | (viii) | Correlation is said to be linear when– (a) | Increase in one variable results in decrease in other variable | (b) | Decrease in one variable results in increase in other variable | (c) | Change in one variable results in change in other variable | (d) | Change in one variable tends to bear constant ratio of change in other variable. | | | (0) |
| | (ix) | Which of the following indices uses only current year quantities as weights – (a) | Bowley’s index number | (b) | Laspeyre’s index number | (c) | Paasche’s index number | (d) | Fisher’s index number | | | (0) |
| | (x) | Which one of the following is not used in the measurement of trend – (a) | semi–average method | (b) | Moving average method | (c) | Least squares method | (d) | Estimation method. | | | (0) |
| (1 mark each) | | |
6. | (a) | Distinguish between any three of the following: | | |
| | (i) | ‘Deliberate sampling’ and ‘random sampling’. | | (0) |
| | (ii) | ‘Classification’ and ‘tabulation’. | | (0) |
| | (iii) | ‘Direct investigation’ and ‘indirect investigation’. | | (0) |
| | (iv) | ‘Historigram’ and ‘histogram’. | | (0) |
| (3 marks each) | | |
| (b) | Re–write the following sentences after filling–in the blank spaces with appropriate word(s)/figure(s) : | | |
| | (i) | "Statistics may be defined as the science of collection, presentation, analysis and interpretation of numerical data."This definition has been given by_______________. | | (0) |
| | (ii) | The___________provides the basis of theory of probability in statistics | | (0) |
| | (iii) | Business forecasting is done with the help of___________statistics. | | (0) |
| | (iv) | ____________are the values of a variable that divide a distribution in to ten equal parts. | | (0) |
| | (v) | Arithmetic mean of 5, 30, 90, 800 and 6,500 is________________. | | (0) |
| | (vi) | The mean of 10 observations is 35. If each observation is multiplies by 5,the changed mean will be______________. | | (0) |
| (1 mark each) | | |
7. | Attempt any three of the following : | | |
| (a) | From the following data, draw the pie chart: Distribution of Rupee Spent on Khadi | Head of Expense | Paise | Farmer Carder and spinner Weaver Washerman, dyer and printer Administrative agency | 19 35 28 8 10 | Total: | 100 | | | (0) |
| (5 marks) | | |
| (b) | Calculate Laspeyre’s, Paasche’s and Fisher’s index numbers for the following data: Item | Base period | Current period | | Qty. | Price | Qty. | Price | A B C D | 12 15 24 5 | 10 7 5 16 | 15 20 20 5 | 12 5 9 14 | | | (0) |
| (5 marks) | | |
| (c) | Find out mean deviation and its coefficient from median of the following data: size(x) frequency (y) | 10 3 | 11 12 | 12 18 | 13 12 | 14 3 | | | (0) |
| (5 marks) | | |
| (d) | From the following data related to two factories, find – (i) | which factory pays larger amount as total wages per hour; and | (ii) | which factory is more variable in wages: Factory A B | No. of Workers 200 250 | Average wage Rs.15 per hour Rs.12 per hour | Variance 16 9 |
| | | (0) |
| (5 marks) | | |
8. | Attempt any three of the following : | | |
| (a) | Write short notes on –(i) Spurious correlation: and (ii) Scatter diagram. | | (0) |
| (5 marks) | | |
| (b) | Calculate Karl Pearson’s coefficient of correlation from the following data and also interpret the result: X 10 12 14 16 18 | Y 20 16 12 8 4 | | | (0) |
| (5 marks) | | |
| (c) | Explain briefly the problems in the construction of index numbers. | | (0) |
| (5 marks) | | |
| (d) | Calculate trend values from the following data using least squares method and estimate the number of workers for the year 2011 : Year No. of Workers (in thousand) | 2006 10 | 2007 12 | 2008 13 | 2009 14 | 2010 16 | | | (0) |
| (5 marks) | | |