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Pune University - FY BSc STATISTICS (Paper - I), April 2010

7 pages, 40 questions, 1 questions with responses, 1 total responses,

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Total No. of Questions : 5] [Total No. of Printed Pages : 7 [3718]-7 F. Y. B. Sc. (Computer Science) Examination - 2010 STATISTICS PAPER - I STATISTICAL METHODS - I (New 2008 Pattern) Time : 3 Hours] [Max. Marks : 80 Instructions : (1) All questions are compulsory. (2) Figures to the right indicate full marks. (3) Use of single memory, non-programmable, scientific calculators and statistical tables is allowed. (4) Symbols have their usual meanings unless otherwise stated. Q.1) Attempt each of the following : (a) [8x2=16] Calculate Mode and Arithmetic Mean of the following data on number of times a batsmen got out on zero in a year for 12 batsmen : 4, 4, 12, 8, 9, 6, 12, 3, 6, 12, 15, 12. (b) Explain the following terms : (i) (ii) (c) [3718]-7 Class Width Open End Class Coefficients of Variation of two groups of observations are 40% and 50% respectively and their Standard Deviations are 16 and 20. Find their Arithmetic Means. 1 P.T.O. (d) If 1 = 0.5 and 2 = 2, find values of 1 and 3. (e) Define Positive Correlation and Negative Correlation with an illustration each for a Bivariate Data. (f) State Expressions for Regression Coefficients in a Bivariate Data. Also, state relationship between Karl Pearson s Coefficient of Correlation and Regression Coefficients. (g) Calculate value of r 12.3 w hen r 12 = 0 .28, r 13 = 0 .5, r23 = 0.49. (h) State four components of Time Series. Q.2) Attempt any four of the following : [4x4=16] (a) Explain Concept of Central Tendency of a Data Set. Discuss median as a measure of Central Tendency. (b) For the following frequency distribution, find median and 8th decile : Wages in Rs. per hour No. of Wage Earners Less than 35 14 35 37 62 37 39 99 39 41 18 41 43 7 Over 43 8 (c) State any four requisites of a good measure of Central Tendency. (d) What is Trimmed Mean ? Discuss its utility. Calculate 20% trimmed mean for a set of ten values : 15, 25, 20, 10, 12, 22, 21, 16, 14, 10. [3718]-7 2 Contd. (e) Write a note on Boxplot. (f) The following is the distribution of sales in thousand Rs. of shops on a street in a city : Sales in thousand Rs. 0-10 10-20 20-30 No. of Shops 14 27 30-40 40 and above 15 If the mode and median of sales are Rs. 24,000 and Rs. 25,000 respectively, find missing frequencies. Q.3) Attempt any four of the following : [4x4=16] (a) What are Relative Measures of Dispersion ? Explain how are they superior to the Absolute Measures of Dispersion ? (b) Given that Arithmetic Mean = 160, Mode = 157, Standard Deviation = 50. Find : (i) Karl Pearson s Coefficient of Skewness (ii) Median (iii) Coefficient of Variation (iv) Comment upon type of Skewness (c) Define rth order raw and central moments for grouped data. How are central moments useful in calculation of measure of Skewness and Kurtosis ? (d) Particulars regarding the income of two localities are given below : Locality X No. of Persons 600 500 Mean Income 175 186 Variance of Income [3718]-7 Locality Y 100 80 3 P.T.O. (i) In which locality is the variation in income more ? Justify your answer. (ii) Find combined standard deviation of the locality X and locality Y put together. (e) Define Skewness. Draw different sketches to indicate different types of Skewness. Which measure of skewness is suitable for frequency distribution with Open End Class. (f) The Standard Deviation of a distribution is 2. What should be the value of 4th Central Moment in order that the distribution is : (i) mesokurtic (ii) platykurtic Q.4) Attempt any two of the following : (a) [2x8=16] (i) What is Scatter Diagram ? Discuss how it is useful in deciding correlation between two variables in a bivariate data. (ii) Compute coefficient of correlation between X and Y for the following data. Interpret your result. X 13 16 19 22 Y (b) 10 21 27 33 39 45 Write stepwise procedure to obtain equation of line of regression of X on Y for a bivariate data. (ii) [3718]-7 (i) In regression analysis the equations of two lines of regression are 8X 10Y + 66 = 0 and 40X 18Y = 214. Find means of X and Y. Also find coefficient of correlation between X and Y. 4 Contd. (c) (i) Discuss Spearman s Rank Correlation for cases with ties and without ties. (ii) Calculate Rank Correlation Coefficient between X and Y, for the following data. Also interpret the result. Marks in Maths Marks in Physics 90 30 42 82 75 45 68 32 45 65 63 40 60 88 90 73 62 66 (d) 85 58 Consider the following data : X Y 4 8 5 12.5 6 18 7 24.5 8 32 Fit a curve of the type Y = aXb using least square principle. Also estimate Y when X = 9. [3718]-7 5 P.T.O. Q.5) Attempt any two of the following : (a) [2x8=16] (i) What is Time Series ? Explain how Time Series Analysis can be considered as a special case of Bivariate Regression Analysis ? (ii) Compute R1.23 and r13.2 for the following data : r12 = 0.7, r13 = 0.5, r23 = 0.5. (b) (i) Describe procedure to estimate seasonal variations in a time series using ratio to trend method. (ii) Estimate trend values using method of five yearly moving average for the following data : Year No. of Students (c) 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 33 31 35 39 40 42 41 43 45 49 A pharmaceutical company employs quality control technique to control concentration of a certain ingredient in their product. Ten samples each of size 3 were taken, which are summerised below : Sample No. 1 2 3 4 5 6 7 8 9 10 X 10.2 10.5 10.4 10.3 9.75 10.2 10.2 10.4 10.3 9.75 R 0.45 0.69 0.53 0.15 0.55 0.24 0.11 0.71 0.9 0.55 Can you say that the process is under statistical quality control using X and R chart ? (For n = 3, A2 = 1.023, D3 = 0, D4 = 2.575) [3718]-7 6 Contd. (d) (i) Describe procedure to locate mode for a grouped frequency distribution using a suitable graph. (ii) Let X1, X2 and X3 be the heights in centimeter of son, his mother and his father measured from their respective means. Find least square equation of plane of regression of X1 on X2 and X3 using the following results : 1 = 2.4, 2 = 2.7, 3 = 2.7, r12 = 0.28, r13 = 0.49, r23 = 0.51 7/7-]8173[

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Additional Info : F.Y. B.Sc. STATISTICS (Paper - I) : Statistical Methods - I (New 2008 Pattern), Pune University
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