Computer Lab - Practical Question Bank
FACULTY OF COMMERCE, OSMANIA UNIVERSITY
---------------------------------------------------------------------------------------------B.Com (Hons) II Year w.e.f.2014-15
QUANTITATIVE TECHNIQUES – II
Paper No. 205
Record
Skill Test
Total Marks
Time: 60 Minutes
: 10
: 20
: 30
1. Calculate Karl Pearson’s coefficient of Skewness for the following data.
25 15 23 40 27 25 23 25 20
2. Calculate Karl Pearson’s coefficient of Skewness for the following data
X
F
0
12
1
17
2
29
3
19
4
8
5
4
6
1
7
0
3. For a group of 10 items X = 452, X2 = 24.270 mode = 43.7 find the Pearson’s
coefficient of Skewness.
4. In a frequency distribution the coefficient of Skewness based upon the quartile is
0.6. if the sum of the upper and lower quartiles is 100 and the median is 38. Find
the values of upper and lower quartile.
5. Find Bowley’s coefficient of Skewness for the following frequency distribution.
X
f
5
9
10
10
15
12
20
15
25
11
30
7
35
6
40
5
45
2
6. Pearson’s coefficient of Skewness for distribution is 0.5 and the coefficient of
variation is 40%. Its mode is 80. Find mean and median of the distribution.
7. Find the first four moments about the arithmetic mean for the following frequency
distribution also find the Kurtosis:
Class
Frequency
0-10
2
10-20
2
20-30
3
30-40
2
40-50
1
8. Compute coefficient of Skewness and Kurtosis based on moments for the
following data:
x
f
4.5
1
14.5
5
24.5
12
34.5
22
44.5
17
54.5
9
64.5
4
74.5
3
84.5
1
9. The first four central moments of a distribution are 0, 2.5, 0.7, 18.75 calculate the
moment measures of Skewness and Kurtosis of the distribution.
94.5
1
10. Find the variance, Skewness and Kurtosis of the following series by the method of
moments:
Class
Frequency
0-10
1
10-20
4
20-30
3
30-40
2
11. Find the coefficient of correlation between the heights of brothers and heights of
sisters from the following data.
Heights of
brothers (in cm)
Heights of
Sisters (in cm)
65
66
67
68
69
70
71
67
68
66
69
72
72
69
12. From the following data compute the coefficient of correlation between x and y.
i)
Arithmetic mean of x series is 25 and that of y is 18
ii)
Sum of the products of deviations of x and y series from their respective
means 122.
iii)
Sum of the squares of deviation from their respective means are 136, 138
respectively for x series and y series
iv)
Number of pairs of values = 15
13. From the data given below, find the number of items ‘n’. If r = 0.5, xy = 120,

y =8, x2 = 90
Where x and y are deviations from arithmetic mean.
14. If N =50, x = 75, y = 80, ,x2 = 150, , y2 = 140, , xy = 120 find the value of ‘r’.
15. A computer operator while calculating the coefficient or correlation between
two variables x and y for 25 pairs of observations obtained the following
constants: n=25, x = 125, x2 = 650, y = 100 , y2 = 460, xy = 508 it was
however later discovered at the time of checking that he had copied down two
pairs as (6,14) and (8,6) while the correct pairs were (8,12) and (6,8) obtain the
correct values of the correlation coefficient.
16. The ranking of ten students in statistics and accountancy are as follows:
Statistics
3
5
8
4
7
Accountancy
6
4
9
8
1
What is the coefficient of rank correlation?
10
2
2
3
1
10
6
5
9
7
17. Calculate the rank correlation coefficient from the data given below:
X
Y
75
120
88
134
95
150
70
115
60
110
80
140
81
142
50
100
18. Eight students have obtained the following marks in statistics and economics.
Calculate the Rank Correlation Coefficient.
Statistics(X)
25
Economics(Y) 50
30
40
38
60
22
40
50
30
70
20
30
40
90
70
19. The coefficient of rank correlation of the marks obtained by 10 students in statistics
and accountancy was found to be 0.8. it was later discovered that the difference
in ranks in the two subjects obtained by one of the students was wrongly taken as
7 instead of 9. Find the correct coefficient of rank correlation.
20. Find the coefficient of correlation ‘r’ when its probable error is 0.2 and the number
of pairs of items is ‘9’.
21. If the value of ‘r’ is 0.9 and its probable error is 0.0128 what would be the value of
‘n’?
22. Calculate probable error, if r = 0.8 and N=7.
23. If two regression coefficients bxy= 0.87 ,byx= 0.49 find ‘r’.


24. Given = 40 x = 10, y = 1.5, rxy = 0.9,
of Y is 10
= 6. Estimate the value of ‘X’ if the value
25. From the following data obtain the two regression equations and calculate the
correlation coefficient.
X
Y
1
9
2
8
3
10
4
12
5
11
6
13
7
14
8
16
9
15
26. From the following data construct the index number for the year 2002 taking 2001
as base by using
Arithmetic mean.
Price (Rs.)
2002
A
6
10
B
2
2
4
6
C
D
10
12
E
8
12
27. Construct index numbers of price from the following data by applying.
Item
Price (Rs.) 2001
a) Laspeyres method
b) Paasche method
c) Bowleys’method
d) Fisher’s ideal method
e) Marshall – Edgeworth method
Current Year
Commodity
Base year 2006
2007
Price
Quantity Price Quantity
A
2
8
4
6
B
5
10
6
5
C
4
14
5
10
D
2
19
2
13
28. Calculate Fisher’s Ideal Index from the data given below and show that it satisfies
time reversal test and factor reversal test.
Commodity
2004
Price
A
B
C
D
10
12
18
20
2005
Quantity Price Quantity
49
12
50
25
15
20
10
20
12
5
40
2
29. Calculate index number by Average of relative method using Arithmetic mean.
Commodity
Price in 1990
Price in 1991
A
6
8
B
10
15
C
2
4
D
12
8
E
5
5
30. An enquiry in to the budgets of middle class families in a family gave the following
information
Expenses on
Price Rs. in 1987
Price Rs. in
2005
Food 30%
100
90
Rent 15
%
20
20
Clothing
20%
70
60
Fuel 10%
20
15
Others
25%
40
55
Compute the price index number using weighted Arithmetic mean of price
relatives.
31. The annual wages (in Rs.) of workers are given along with consumer price indices
find
i)
The real wages
Year
Wages
Consumer price
Index
ii) Real wage indices
2000
1800
100
2001
2200
170
2002
3400
300
2003
3600
320
32. From the chain base index number given below prepare fixed base index
numbers.
Year 2000 2001
2002
2003
2004
CBI
80
110
120
90
140
33. Construct the cost of living index numbers from the table given below:
Group
Food
Clothing
Fuel
Rent
miscellaneous
Index for
2005
550
220
215
275
150
Expenditure
46%
7%
10%
25%
12%
34. Prepare the consumer price index for 2006 on the basis of 2005 from the following
data by
(a) Aggregate Expenditure method
b) family budget method and also show
that consumer price index is same for both the methods.
Commodities
A
B
C
Quantities consumed in
2005
6
6
1
Prices in
2005
5.75
5.00
6.00
Prices in
2006
6.00
8.00
9.00
D
E
F
6
4
1
10.00
1.50
15.00
8.00
2.00
20.00
35. From the following data find the percentage increase in the food. It is given that
the cost of living index number in the year 1999 is 204.6
Group
Price increases in
percentage of 1999
Food
?
Rent
80
Clothing
200
Fuel
120
miscellaneous
125
weight
50
26
10
8
6
36. Calculate five- yearly moving averages of number of students studying in a
college from the following figures.
Year
1981
No. of
332
Students
1982
317
1983
357
1984
392
1985
402
1986
405
1987
410
1988
427
1989
405
1990
438
37. Determine the equation of a straight line which best fits the following data;
Year
2000
2001
2002
2003
2004
Sales (in Rs.)
35
56
79
80
40
Compute the trend values for all the years from 2000 to 2004.
38. Calculate the seasonal index for the following data by using simple average
method.
Year
1st Quarter
2001
2002
2003
2004
2005
72
76
74
76
78
2nd
Quarter
68
70
66
74
74
3rd Quarter
80
82
84
84
86
4th
Quarter
70
74
80
78
82
39. Calculate seasonal indices for each quarter from the following percentages of
whole sale price indices to their moving averages.
Year
2001
2002
2003
2004
2005
I
-12.5
16.8
11.2
10.5
Quarter
II
III
-11
13.5
15.5
15.2
13.1
11
12.4
13.3
--
IV
11
14.5
15.3
13.2
--
40. A bag containing 10 white, 15 red 8 green balls a single draw of 3 ball is made.
a) What is the probability that white, red, green balls are drawn?
b) What would be the probability of getting the entire three white balls?
41. A card is drawn from an ordinary pack of playing cards and a person bets that it
is a spade or an ace. What is the probability of his winning this bet?
42. A problem in statistics is given to three students A,B,C whose chances of solving it
are ½, ¾, ¼ respectively what is the probability that problem is solved.
43. The probability that a student passes a physics test is (2/3) and the probability that
he passes both physics and English test is (14/45). The probability that he passes at
least one test is (4/5). What is the probability that the student passes the English
test?
44. A piece of equipment will function only when all three parts A, B, Care working.
The probability of part A failing during one year is (1/6) that of B failing is (1/20)
and that of ‘c’ failing is (1/10) what is the probability that the equipment will fail
before the end of the year?
45. A bag contains 5 white and 3 black balls. Two balls are drawn at random one
after the other without replacement. Find the probability that both the balls
drawn are black.
46. In a Binomial distribution the mean and standard deviations are 12 and 2
respectively find n and p.
47. 8 coins are tossed at a time, 256 times find the expected frequencies of success
(getting a head).
48. Find the binominal distribution whose mean is 3 and variance is 2.
49. Assuming that the typing mistake per page committed by a typist follows a
poisson distribution find the expected frequencies for the following distribution of
typing mistakes:
No. of mistakes per page 0
No. of pages
40
1
30
2
20
3
15
4
10
5
5
50. The marks obtained in a certain examination follow normal distribution with mean
45 and standard deviation 10. If 1000 students appeared at the examination.
Calculate the number of students scoring (a) less than 40 marks and (b) more
than 60 marks.