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Section A

1. Attempt any SIX parts: 6 i) What is PRIMARY DATA?

ii) What is TABULATION?

iii) Define MEAN.

iv) What is meant by SYMMETRY and SKEWNESS?

v) What is meant by REGRESSION? vi) What is MULTIPLE CORRELATION? vii) What is Principle of LEAST SQUARE? viii) Define INDEX NUMBER. ix) What is meant by DETRENDING?

Section B

n

    1. a) Find the A.M, G.M and H.M of the series 1, 2, 4, 8, 16, ….., 2 . 4

    2. b) The mean and geometric mean of three numbers are 34 and 18 respectively. Find all three numbers when the G.M. of first two numbers is 9. 4
  1. a) Derive the relations which give the third and fourth moments about the mean in terms of moments about the origin. 4

b) Following information regarding the two sets of data. n= 150 Ó(x– 100) = 180, Ó(x– 100)2 = 245320 ,

11 1

n= 200 Ó(x– 100) = 250, Ó(x– 100) 2 = 43850 ,

22 2

i) Which of the distribution is more consistent? ii) Find Combined coefficient of variation.

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4. a)Provethatthesimpleaggregativevalueindex number (satisfies the time reversal and the circular test but do not satisfy

Ópoqo

the factor Reversal test. 4 b) A textile worker in a certain city spends Rs. 350 per month. The cost of living index for a particular month is 136. Using the following data find the amount he spends on housing and clothing. 4

Item Food Clothin g Housing Fuel M isc.
E xpen diture 140 X Y 56 63
Inde x No. 180 150 100 110 80
    1. a) Calculate a seven days moving averages from the following record of attendance:

    2. b) Find the seasonal indices by ratio-to-trend by fitting a straight line using annual averages by taking the origin at the middle of 1962 and 1963.
    1. a) Derive the normal equation of the straight line. 4 b) Fit a curve of the type y = aebx from the following data. 4

    2. ÓX2 -aoÓX -boÓXY

  1. a) Show that S =

W eek Sun M on T ue W ed T hu Fri Sat
I 24 55 29 48 52 55 61
II 27 52 32 43 53 56 63
Year Qu arters
I II III IV
1961 122 125 118 117
1962 119 114 114 109
1963 105 99 93 89
1964 86 80 83 84
X 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Y 1.1 1.3 1.6 2.0 2.7 3.4 4.1

4

x.y

n -2 b) Fit a regression line of Y on X from the data 4

X 3.2 2.7 4.5 1.0 2.0 1.7 0.6 1.9
Y 6.5 5.3 8.6 1.2 4.2 2.9 1.1 3.2

Also compute i) TOTAL VARIATION ii) EXPLAINED VARIATION iii) UNEXPLAINED VARIATION

8. a) Show that Correlation Coefficient always lies between -1 and +1.

b)CalculatetheMULTIPLECORRELATIONR1.23 andPARTIALCorrelation Coefficient ã12.3 from thedatagiven below: 4 b21 = -0.1 b12 = -0.4 b31 = 0.27 b13 = 0.6 b23 = 0.38 b32 = 0.67

*** B.A/B.Sc – I (09/A) xi ***

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last updated on 28-04-2019