Madras University Question Paper

Subject : BUSINESS MATHEMATICS AND STATISTICS

Subject Code : MWG

OCTOBER 2013 U/ID 1370/MWG

Time : Three hours Maximum : 100 marks

SECTION A — (5 × 8 = 40 marks)

Answer any FIVE questions.

All questions carry equal marks.

1. In a survey of 5,000 persons, it was found that

2,800 read Indian Expenses and 2,300 read states

man while 400 read both papers. How many do not

read neither Indian expenses nor states man?

2. The average monthly income of a person for the

first eight months of a year exceeds that of the

first seven months of the year by Rs.25. If he earns

Rs.1,275 in the eighth month of the year, find his

average monthly income for the first eight months

of the year.

(8 pages)

3. A person borrowed Rs.500 from a money lender

and agree to pay four instalments of Rs.150 each

at the end of 3, 6, 9, 12 months. Find the rate of

simple interest per annum charged by the money

lender.

4. Construct a table with suitable class interval for

the following data.

28 30 34 39 18 19 20 40 50 70

14 24 60 66 88 78 70 72 64 56

64 42 36 30 30 25 27 29 30 41

45 47 49 51 59 40 65 64 62 59

18 20 22 34 44 47 48 50 45 40

5. From the following data compute the value of

upper and lower quartiles.

Marks No. of

students

Below – 10 8

10 – 20 10

20 – 40 22

40 – 60 25

60 – 80 10

Above 80 5

Total 80

6. Explain about various methods of constructing

index numbers.

7. What are the advantages of stratified random

sampling?

8. An integer is chosen at random out of the integers

from 1 to 100. What is the probability that, it is

(a) multiple of 5

(b) divisible by 7

(c) greater than 70.

SECTION B — (3 × 20 = 60 marks)

Answer any THREE questions.

All questions carry equal marks.

9. A man retires at the age of 60 and earns a pension

of Rs.8,700 a year. He wants to commute one third

of his pension. Find the amount he will receive, if

the expectations of his life at this age be 10 years,

and the interest is compounded at 4% per annum.

(Assume that pension for a year is due at the end

of the year).

10. Find the standard deviation for the following

distribution :

X : 4.5 14.5 24.5 34.5 44.5 54.5 64.5

f : 1 5 12 22 17 9 4

11. Two judges in a beauty competition rank the 12

entries as follows :

X : 1 2 3 4 5 6 7 8 9 10 11 12

Y : 12 9 6 10 3 5 4 7 8 2 11 1

What degree of agreement is there between the

judgement of the two judges?

12. Calculate the cost of living index number using

aggregate expenditure method :

Commodity Unit consumption in

base year

Price in

base year

Price in

current year

Wheat 200 1.0 1.2

Rice 50 3.0 3.5

Pulses 50 4.0 5.0

Ghee 20 20.0 30.0

Sugar 40 2.5 5.0

Oil 50 10.0 15.0

Fuel 60 2.0 2.5

Clothing 40 15.0 18.0

13. Below are given the figures of production (in

thousand quintals) of a sugar factory :

Year Production

(thousand quintals)

1989 77

1991 88

1992 94

1993 85

1994 91

1995 98

1998 90

Fit a straight line and tabulate the trend values.

———————

Subject : BUSINESS MATHEMATICS AND STATISTICS

Subject Code : MWG

OCTOBER 2013 U/ID 1370/MWG

Time : Three hours Maximum : 100 marks

SECTION A — (5 × 8 = 40 marks)

Answer any FIVE questions.

All questions carry equal marks.

1. In a survey of 5,000 persons, it was found that

2,800 read Indian Expenses and 2,300 read states

man while 400 read both papers. How many do not

read neither Indian expenses nor states man?

2. The average monthly income of a person for the

first eight months of a year exceeds that of the

first seven months of the year by Rs.25. If he earns

Rs.1,275 in the eighth month of the year, find his

average monthly income for the first eight months

of the year.

(8 pages)

3. A person borrowed Rs.500 from a money lender

and agree to pay four instalments of Rs.150 each

at the end of 3, 6, 9, 12 months. Find the rate of

simple interest per annum charged by the money

lender.

4. Construct a table with suitable class interval for

the following data.

28 30 34 39 18 19 20 40 50 70

14 24 60 66 88 78 70 72 64 56

64 42 36 30 30 25 27 29 30 41

45 47 49 51 59 40 65 64 62 59

18 20 22 34 44 47 48 50 45 40

5. From the following data compute the value of

upper and lower quartiles.

Marks No. of

students

Below – 10 8

10 – 20 10

20 – 40 22

40 – 60 25

60 – 80 10

Above 80 5

Total 80

6. Explain about various methods of constructing

index numbers.

7. What are the advantages of stratified random

sampling?

8. An integer is chosen at random out of the integers

from 1 to 100. What is the probability that, it is

(a) multiple of 5

(b) divisible by 7

(c) greater than 70.

SECTION B — (3 × 20 = 60 marks)

Answer any THREE questions.

All questions carry equal marks.

9. A man retires at the age of 60 and earns a pension

of Rs.8,700 a year. He wants to commute one third

of his pension. Find the amount he will receive, if

the expectations of his life at this age be 10 years,

and the interest is compounded at 4% per annum.

(Assume that pension for a year is due at the end

of the year).

10. Find the standard deviation for the following

distribution :

X : 4.5 14.5 24.5 34.5 44.5 54.5 64.5

f : 1 5 12 22 17 9 4

11. Two judges in a beauty competition rank the 12

entries as follows :

X : 1 2 3 4 5 6 7 8 9 10 11 12

Y : 12 9 6 10 3 5 4 7 8 2 11 1

What degree of agreement is there between the

judgement of the two judges?

12. Calculate the cost of living index number using

aggregate expenditure method :

Commodity Unit consumption in

base year

Price in

base year

Price in

current year

Wheat 200 1.0 1.2

Rice 50 3.0 3.5

Pulses 50 4.0 5.0

Ghee 20 20.0 30.0

Sugar 40 2.5 5.0

Oil 50 10.0 15.0

Fuel 60 2.0 2.5

Clothing 40 15.0 18.0

13. Below are given the figures of production (in

thousand quintals) of a sugar factory :

Year Production

(thousand quintals)

1989 77

1991 88

1992 94

1993 85

1994 91

1995 98

1998 90

Fit a straight line and tabulate the trend values.

———————

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