HOLY CROSS COLLEGE(Autonomous) TIRUCHIRAPPALI 620 002B.Sc. DEGREE EXAMINATION, SEMESTER I, NOVEMBER 2014ALLIED 1: MATHEMATICAL STATISTICS IMODEL QUESTION PAPERTime: 3 HoursCode: U10MA1ACT01 Max.Marks: 100SECTION AANSWER ALL THE QUESTIONS:Choose the correct answer:1. The central value of a class interval is called (a) mid-point (b) upper limit(c)lower limit (d) both upper and lower limits2.A histogram is used to present frequency distribution of (a) discrete data (b) continuous data (c) any of discrete or continuous (d) both discrete and continuous 3.The formula for range is(a) (b) (c) (d) ( ) ( ) 4. The coefficient of skewness is (a) (b) (c) (d) 5.The coefficient of correlation always lies between (a) 0 and 1 (b) -1 and 0 (c) -1 and + 1 (d) -2 and + 26.The regression coefficient of x on y is(a) r (b) r (c) (d)

7. The best method of computing index number is(a) Laspeyres method (b) Pasches method (c)Bowleys method (d) Fishers ideal method8.Fishers ideal index satisfies (a) time reversal test (b) Factor reversal test (c) either (a) or (b) (d) neither (a) nor (b)9.Match the following classification of statistical data with its corresponding nature and choose the correct answer:1. indispensable tool in all aspects of economics(A) indirect oral interview 2. An age of planning (B) Modern age 3.Collection of primary data (C) Questionnaire 4.The media communication between (D) Statistics investigator and respondents (E)(a) 1A,2B,3D,4C (b)1D,2B,3C,4A (c)1D,2B,3A,4C(d)1C,2E,3A,4B

10. Of the following pair of statements one is an assertion and the other is a possible reason. Read them carefully and mark your answer according to the key.Assertion :An index number is a number which is used to measure the level of a certain phenomenon.Reason :An index number is a statistical device for comparing the general level of magnitude of a group of related variables in two or more situations. a. Both assertion and reason are true statements and the reason explains the assertion. b. Both assertion and reason are true statements and the reason does not explain the assertion. c.Assertion is true but the reason is false. d. Both are false statements.Write short answers for the following questions:11.Write the two categories of secondary data.12.Define diagram.13.What is the third moment about mean?14.What does the measure of kurtosis indicate?.15.Define negative correlation.16.Mention rank correlation if two judges have common taste.17.When is an index number said to be good?18.What is meant by quantity index number?19.Define time series.20.Write any two types of trend.

SECTION BANSWER ALL THE QUESTIONS, CHOOSING ONE FROM EACH SET: 5X7=3521(a).Explain any one method of collecting primary data. OR21(b)Draw a pie diagram to represent the following data which shows the area in millions of square kilometers of the oceans of the world.OceanArea(million sq. km)

Pacific70.8

Atlantic41.2

Indian28.5

Antarctic7.6

Arctic4.8

22(a)Calculate standard deviation from the following data:Marks:102030405060No. of students: 8122010 7 3 OR

22(b)Calculate Karl Pearsons coefficient of skewness for the following distribution:x : 0-5 5-1010-1515-2020-2525-3030-3535-4023(a)Calculate the correlation coefficient between X and Y where X height of father; Y-height of son;X:64656667686970Y:66676568706872OR23(b)Given the data below, calculate the value of Y when X = 12 by finding regression equation of Y on X.XYAverage7.614.8Standard deviation3.62.524(a)Calculate Laspeyres and Paaches price indices from the data given below:CommodityPriceQuantity

2002200320022003

ABCD 812 6 41015 8 6201016 830102010

OR24(b)Construct chain index numbers from the link relatives given below:Year:20002001200220032004Link Index: 100 105 95 115 10225(a)Calculate trend values for 2002 and 2003 by the method of least squares from the data given below:Year:20022003200420052006Sales (in lakhs): 70 74 80 86 90 OR25(b)Calculate seasonal indices by simple average method for the data given below:YearProduction

1 234

20013.53.93.43.6

20023.54.13.74.0

20033.53.93.74.2

20044.04.63.84.5

20054.14.44.24.5

SECTION CANSWER ANY THREE OF THE FOLLOWING:3 x 15 = 4526(a).Draw simple bar diagram to represent the following data:(8 Marks)Class:0-1010-2020-3030-4040-5050-6060-7070-8080-90Frequencies:4571416148165 (b)Write the differences between diagrams and graphs.(7 Marks)27(a)Find quartile deviation from the following data:(8 Marks)X:100-200200-300300-400 400-500 500-600f:48189884728 (b)Calculate mean deviation about mode from the following:(7 Marks)X:2.57.512.517.522.527.5f:1928502210728(a)Compute Spearmans rank correlation coefficient from the following data: (8 Marks)Wages:1001011021021009997989695Cost of living:98999997959295949091

28(b)Obtain regression line of Y on X from the following data: (7 Marks)X:101213121615Y:403843453743`29(a)Convert the following fixed base index (FBI) numbers into chain base index numbers(CBI)( 8 Marks)Year:199019911992199319941995FBI:376392408380392400 (b)Show that Fishers index number is an ideal index number for the following data.(7 Marks)Commodity20062007

PriceQuantityPriceQuantity

ABCD 1012 18 204925 10 5121520 405020122

30.Calculate the seasonal indices by link relative method from the following data:QuartersYearQ1Q2Q3Q4197865585661197968636367198070595652198160555158 ********************************************