GSEB Std 12 General Question Paper 2020 Statistics (English Medium)

Gujarat Secondary and Higher Secondary Education Board, Gandhinagar Unit Test Standard: 12th (General Stream) Max. Marks: 25 Subject: Statistics (135) Time: 1 hour ➢ There are total 11 questions in this test. ➢ Students have to write the answers of this unit test in their notebook. SECTION A  Choose the correct alternatives from the following options: [1 mark each] [03] 1. Which method is useful to compare the long term variations in the values of the variable? (a) Chain Base Method (b) Laspeyre’s Method (c) Fixed Base Method (d) Paasche’s Method 2. What is the range of the correlation coefficient r? (a) −1 < 𝑟 < 1 (b) 0 to 1 (c) −1 ≤ 𝑟 ≤ 1 (d) -1 to 0 3. The regression line always passes through which point? (a) (𝑥̅ , 𝑦̅) (b) (0, 𝑦̅) (c) (𝑥̅ , 0) (d) (0, 0) SECTION B  Answer the following questions as required: [1 mark each] [03] 4. What is base year? 5. Define Correlation. 6. The regression coefficient is not independent of which transformation? SECTION C  Answer the following questions as required: [3 marks each] [09] 7. The chain base index numbers for sales of a certain type of scooter from the year 2010 to 2015 are as follows. Find fixed base index numbers. Year 2010 2011 2012 2013 2014 2015 Index Number of Sale 110 112 109 108 105 111 8. The singing talent of five singers A, B, C, D and E was judged by two judges in a singing competition. The ranks assigned to five singers are as follows. Rank 1 2 3 4 5 By Judge 1 C A B E D By Judge 2 B C D A E Find the similarity between the decisions of the two judges from the rank correlation coefficient.

9. The information of investment (in lakh Rs.) and its market price (in lakh Rs.) after six months in share market in the last seven years for a Mutual Fund Company is obtained as follows: Market Price after six months (lakh Investment (lakh Rs.) Particulars Rs.) x y Mean 40 50 Variance 100 256 Covariance = 80 Obtain the regression line of Y on X and estimate the market price in the share market after six months if there is an investment of Rs. 45 lakh in a year. SECTION D  Answer the following questions as required: [5 marks each] [10] 10. Compute the Laspeyre’s, Paasche’s and Fisher’s index numbers for the year 2015 from the data given below: Quantity Price (Rs.) Item Year 2014 Year 2015 Year 2014 Year 2015 A 25 kg 32 kg 42 45 B 15 litre 20 litre 28 30 C 10 pieces 20 pieces 30 36 D 8 meter 15 meter 20 25 E 30 litre 36 litre 60 65 11. Find Karl Pearson’s Correlation Coefficient between density of population (per square km) and death rate (per thousand) from the following data City A B C D E F G Density (per sq. km) 750 600 350 500 200 700 850 Death rate (per thousand) 30 20 15 20 10 25 50 OR 11. To study the relationship between the time of usage of cars and its average annual maintenance cost, the following information is obtained: Car 1 2 3 4 5 6 Time of usage of a car (years) x 3 1 2 2 5 3 Average annual maintenance cost (thousand Rs.) y 10 5 8 7 13 8 Obtain the regression line of Y on X. Find an estimate of average annual maintenance cost when the usage time of a car is 5 years. Also find its error.