B.Sc. (Part (Semester II) (CBCS Pattern) Examination, 2018
Paper VIII Descriptive Statistics II
Day and Date Wednesday, 28-11-2018 Max. Marks 70
Time 10.30 a.m. to 1.00 p.m.
Instructions All questions are compulsory.
ii) Figures to right indicate full marks.
iii) Use of any type of calculator is allowed.
1. Select most correct alternative 14
The idea of product of moment correlation coefficient was given by
R. A. Fisher Francis Galton
Karl Pearson Spearman
If r the two variables are
Linearly related Dependent
Not lineraly related None of the above
If byx then bxy is
Less than 1 Greater than 1
Equal to 1 Not certain
Relation between correlation coefficient and regression coefficient is
r b b xy yx ∗ (with sigh of regression coefficient)
r (with sign of regression coefficient)
r bxy*byx (with sign of regression coefficient)
bxy/byx (with sign of regression coefficient)
Range of correlation coeffient is
0 to 1 1 to 1 0 to ∞ ∞ to
If r12 0 and r13 0 then r12.3 is equal to
1 0
0.5 None of the above
The range of R1.23 is
0 to 1 1 to
1 to 0 None of the above
If r then bxy is
Positive Negative
Not certain None of these
Laspeyre's price index formula uses as the weights.
Current year's quantities Base year's prices
Current year's prices Base year's quantities
10) The time series data is arranged
Geographically Qualitatively
Quantitatively Chronologically
11) Fisher index number is mean of Laspeyre's and Passche's
index number.
Geometric Arithmetic
Harmonic None of the above
12) Variation due to earthquakes is belongs to
Cyclic variation Secular trend
Irregular variation None of the above
13) If the line of regression of Y on X and X on Y are X Y 15 and X 2Y 20
respectively, then A.M. of X is
10 05
7.5 None of these
14) The variation in sales of cotton clothes is attached to the component of
the time series
Secular trend Seasonal variation
Cyclical variation All of these
2. Attempt any seven of the following 14
Define Fisher price index number.
Write the interpretation of correlation coefficient if r r r 0.
If Σd1
2 416, n 12 then find the value of rank correlation.
Define index number.
Define Regression.
If r12 0.7, r13 r23 0.5 find r12.3.
Explain the concept of Index Number.
If Cov 13.0 and σx 3.60 and σy 4.07 then find value of r.
Define Karl Pearson's coefficient of correlation.
3. Attempt any two of the following 10
Ten students got following marks in Math's and Stat.
Math's 8 36 98 25 75 82 92 62 65 35
Stat 84 51 91 60 68 62 86 58 35 49
Find the Spearman's Rank correlation and give conclusion.
Compute 3 year moving average for following data.
Year 1 2 3 4 5 6
Sales 14 15 10 8 9 11
For the following data fit straight line trend by least square method and
estimate value for year 2007.
Year 2000 2001 2002 2003 2004 2005
Profit 83 92 71 90 160 191
Discuss the irregular variation in Time Series. 4
4. Attempt any two of the following 14
The two lines of regression are 3X Y 5 0 and 4X 3Y 0.
Find the mean of X and Y.
II) Correlation between X and Y.
Find Fisher price index number for following data
Products
Year 2014 Year 2016
Price Quantity Price Quantity
A 60 300 100 560
B 20 200 20 240
C 40 240 60 360
D 100 300 120 300
E 80 320 120 450
Explain the concept of Partial correlation.
5. Attempt any two of the following 14
Explain the concept of scatter diagram.
If x1, x2, x3 are the variables, such that
σ1 2.4, σ2 2.7, σ3 2.7, r12 0.20, r13 0.40, r23 0.50, X1 30,
X2 35, X3 48 then obtain the equation of regression x1 on x2 and x3.
For the following data obtain the two lies of regression by using method
of least square method. Also obtain the value of Y when X 9
X 1 5 3 2 1 1 7 3
Y 6 1 0 0 1 2 1 5