5. | (a) | State, with reasons in brief, whether the following statements are true or false : | | |
| | (i) | Statistics have no limitations. | | (0) |
| | (ii) | Mode is affected by extreme observations. | | (0) |
| | (iii) | Value of standard deviation is only positive. | | (0) |
| | (iv) | Secular trend variations are of regular nature and repeat after a fixed interval of time. | | (0) |
| | (v) | Same weight is given to all commodities in a weighted index number. | | (0) |
| (2 marks each) | | |
| (b) | Write the most appropriate answer from the given options in respect of the following: | | |
| | (i) | "Statistics may be defined as the science of collection, presentation, analysis and interpretation of numerical data." This definition of statistics was given by – (a) | Lovin | (b) | Croxton and Cowden | (c) | A. L. Bowley | (d) | King. | | | (0) |
| | (ii) | Frequency of a class per unit width that indicates concentration of frequency in the class is known as– (a) | Frequency distribution | (b) | Frequency density | (c) | Class width | (d) | Class interval. | | | (0) |
| | (iii) | Index numbers that measure the changes in total money worth during some period compared with other period are known as – (a) | Quantity index numbers | (b) | Value index numbers | (c) | Wholesale price index numbers | (d) | Retail price index numbers. | | | (0) |
| | (iv) | In case of a symmetrical distribution – (a) | Mean = median = mode | (b) | Mode = 3 median – 2 mean | (c) | Mode/median = mean | (d) | Mode – mean = median. | | | (0) |
| | (v) | Harmonic mean of 400, 100, 300, 200 is –: (a) | 250 | (b) | √1000 | (c) | 192 | (d) | (250)2 | | | (0) |
| | (vi) | The organisations such as Reserve Bank of India (RBI) and National Sample Survey Office (NSSO) collect and publish – (a) | Derivative data | (b) | Mixed data | (c) | Secondary data | (d) | Primary data. | | | (0) |
| | (vii) | The correlation co–efficient lies between – (a) | –1 and +1 | (b) | 0 and +1 | (c) | 0 and – 1 | (d) | + 1 and + 2. | | | (0) |
| | (viii) | Seasonal variations are absent if the time interval between successive observations is – (a) | Less than or equal to one year | (b) | Equal to one year | (c) | More than one year | (d) | None of the above. | | | (0) |
| | (ix) | In any pie–chart, the sum of central angle is – (a) | 90 degree | (b) | 180 degree | (c) | 270 degree | (d) | 360 degree. | | | (0) |
| | (x) | Which one of the following is a positional average – (a) | Arithmetic mean | (b) | Geometric mean | (c) | Median | (d) | Harmonic mean. | | | (0) |
| (1 mark each) | | |
6. | (a) | Distinguish between any three of the following: | | |
| | (i) | ‘Harmonic mean’ and ‘geometric mean’. | | (0) |
| | (ii) | ‘Primary data’ and ‘secondary data’. | | (0) |
| | (iii) | ‘Census investigation’ and ‘sample investigation’. | | (0) |
| | (iv) | ‘Dorbish and Bowley’s index number’ and ‘Fisher’s ideal index number’. | | (0) |
| (3 marks each) | | |
| (b) | Re–write the following sentences after filling–in the blank spaces with appropriate word(s)/figure(s) : | | |
| | (i) | The word ‘statistics’ is used in two senses, i.e., statistical data and ____________. | | (0) |
| | (ii) | In __________ classification, data are classified on the basis of certain characteristics or presence and absence of attributes like intelligence, honesty, occupation, etc. | | (0) |
| | (iii) | ________of a distribution divides a series of observations into 100 equal parts. | | (0) |
| | (iv) | In an approximate normal distribution x – ± 2σ covers about __________ of the distribution | | (0) |
| | (v) | The study of association between two characteristics can be divided into two broad categories, i.e., correlation and ____________. | | (0) |
| | (vi) | _____________ of data implies the removal of the effect of seasonal variations. | | (0) |
| (1 mark each) | | |
7. | Attempt any three of the following : | | |
| (i) | "The two ogives intersect at median." Define ‘ogive’ and elaborate the statement with the help of an example. | | (0) |
| (ii) | Explain Spearman’s rank correlation method. | | (0) |
| (iii) | "Forecasting can be done on the basis of collection of data or obtaining opinion of the experts." Explain. | | (0) |
| (iv) | From the following, find seasonal indices (upto two decimal places) by using moving average method : year | Quater 1 | Quater 2 | Quater 3 | Quater 4 | 2005 2006 2007 2008 2009 | 30 23 24 21 25 | 20 25 23 45 35 | 25 30 29 26 40 | 27 20 21 19 25 | | | (0) |
| (5 marks each) | | |
8. | Attempt any three of the following : | | |
| (i) | Represent the following data by histogram : Class interval Frequency | 0–50 12 | 50–100 5 | 100–150 22 | 150–200 3 | 200–250 15 | 250–300 7 | | | (0) |
| (ii) | Find the co-efficient of correlation between the marks obtained by 12 students of a post–graduate course in two papers of Economics and Statistics of 100 marks each from the following by using the method of calculating co-efficient of correlation by assuming mean. Also comment upon the co–efficient of correlation so arrived : Marks in Economics | 75 | 80 | 75 | 83 | 78 | 84 | 85 | 60 | 79 | 74 | 81 | 77 | Marks in Statistics | 79 | 85 | 70 | 80 | 80 | 90 | 88 | 63 | 87 | 73 | 82 | 76 | | | (0) |
| (iii) | The mean of a certain number of observations is 50. If three numbers 70, 60 and 65 are added to this data, the mean rises to 55. Find the number of items in the original data ? | | (0) |
| (iv) | The following is the distribution of aggregate percentage of marks of students in a class : Aggregate marks (%) | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 | Number of Students | 1 | 3 | 10 | 20 | 15 | 6 | 5 | Calculate the percentage of students having the range x – ±σ? | | (0) |
| (5 marks each) | | |