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CLASS: B.Com.
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS – APRIL 2010
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
IV
2008
08UCO430404
ALLIED OPT: ELEMENTS OF STATISTICS
SECTION – A
Answer all the questions:
20 x 1 = 20
Choose the correct answer:
1.
2.
The median of 8, 10, 5, 9, 12, 11 is
a)
9
b)
10
c)
9.5
d)
10.5
b)
Mean  Median
S.D
Mean  Mode
Median
The Karl Pearson’s coefficient o skewness is
a)
c)
3.
c)
5.
d)
The probability of getting 6 in the first die
a)
4.
Mean  Mode
S.D
3(Mean  Mode)
S.D
1
36
5
36
b)
d)
2
36
1
6
The index number which is from arithmetic mean of Laspeyro’s and Paasche’s method is
a)
Fisher’s Ideal Method
b)
Bowley Dorfish method
c)
Klalsch’s method
d)
Kethey’s method
The formula is used when figures to be interpolated is in the middle of the series
a)
Newton’s difference formula
b)
Newton’s forward formula
c)
Newton’s backward formula
d)
None of these
State True or False:
6.
Mean – Median = 3(Mean – Mode)
7.
Coefficient of Mean deviation is
Mean deviation
.
Median
8.
When thins are arranged in a circle, we find two ends in each arrangement.
9.
In free – hand method, the sum of the squares of the vertical deviations from the trend should
be as large as possible.
10.
Newton’s divided difference method is used when the value of independent variable x
advances by unequal intervals.
Fill in the blanks:
11.
The data are classified according to some characteristic is known as ______ classification.
12.
The value of the coefficient of correlation lie between ______ and ______.
13.
If the events are not mutually exclusive then P (A B) = ______.
14.
The general tendency of the time series data to increase or decrease or stagnets during a long
period of time is called ______.
15.
Newton’s formula for interpolating the value of y for a given value of x is ______.
Answer in one or two sentences:
16.
Define secondary data.
17.
Find the
40, 43.
18.
Define equally likely events.
19.
Say anyone essential requirement of time series.
20.
What are the two major methods of Interpolation.
range
of
weights
of
7
students
from
27,
40,
35,
36,
SECTION – B
Answer all the questions:
21.
a.
5 x 4 = 20
What are the rules of classification. Explain it.
OR
b.
Calculate the median from the following table.
Marks
Frequency
10-25
25-40
40-55
55-70
70-85
85-100
6
20
44
26
3
1
38,
22.
a.
For a group of 50 male workers, the mean and the standard deviation of their waves
are Rs.63 and Rs.9 respectively. For a group of 40 female workers these are Rs.54
and Rs.6 respectively. Find the standard deviation for the combined group of 90
workers.
OR
b.
23.
a.
Find Karl Pearson’s coefficient of correlation from the following data.
Wages
100
101
102
102
100
99
97
98
96
95
Cost of
living
98
99
99
97
95
92
95
94
90
91
A bag contains 7 red balls and 5 white balls. 4 balls are drawn at random. What is
the probability that (i) all of them are red. (ii) two of them are red and two white?
OR
b.
The odds in favour of a certain event are 2 to 5 and the odds against another event
independent of the former are 5 to 6. Find the chance that one atleast of the events
will happen.
24.
a.
Explain briefly about the two types of the time series models.
OR
b.
An enquiry into the budgets of middle class families in a certain city gave the
following information.
Expenses
Food
35%
Fuel
10%
Cloth
20%
Rent
15%
Miscellaneous
20%
Prices (Rs) (1995)
150
25
75
30
40
Prices (Rs) (1996)
145
23
65
30
45
What is the cost of living index number of 1996 as compared with that of 1995?
25.
a.
Interpolate the figure of population for the year 1996 from the following data :
Year
Population
of a town
1960
1970
1980
1990
25,494
29,003
32,528
36,070
OR
b.
Use Lagrange’s interpolation formula to find y when x = 0, given the following
table.
x
-1
-2
2
4
y
-1
-9
11
69
SECTION – C
Answer any FOUR questions:
26.
27.
The frequency distribution of weight in grams of mangoes of a given variety is given below.
Calculate the arithmetic mean, median and mode.
29.
Weight
(in gms)
No of mangoes
Weight
(in gms)
No. of mangoes
410 – 419
14
450 – 459
45
420 – 429
20
460 – 469
18
430 – 439
42
470 – 479
7
444 – 449
54
Calculate Karl Pearson’s coefficient of skewness for the following data
25
28.
4 x 15 = 60
15
23
40
27
25
23
25
20
Two dice are thrown. Find the probability that
a.
the sum of the numbers shown by the dice is exactly 6.
b.
the total of the numbers on the dice is greater than 8.
c.
the total of the numbers on the dice is greater than 8.
d.
the total of the numbers on the dice is 13.
e.
the first die shoes 6.
The following table gives the sterling assets of the R. B. I in crores of rupees.
a.
Represent the data graphically
b.
Fit a straight line trend.
c.
Show the trend on the graph.
Year
1986-87
1987-88
1988-89
1989-90
1990-91
1991-92
Assets
83
92
71
90
Also estimate the figures for 1996-97.
30.
From the following table, estimate the value of y when x = 65
x
31
41
51
61
71
y
46
66
81
93
101
**************
169
191