# Quantitative Techniques In Management

Quantitative Techniques in Management

Assignment A

1. From the following data calculate the missing the missing frequency. No. of

tablets

4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40

No. of

Persons

Cured

11 13 16 14? 9 17 6 4

The average number of tablets to curve fever was 19.9.

Solution:

No. of tablets

Mid point

No. of persons cured

Product

4-8

6

11

66

8-12

10

13

130

12-16

14

16

224

16-20

18

14

252

20-24

22

x

22x

24-28

28-32

26

30

9

17

234

510

32-36

34

6

204

36-40

38

4

152

1772+22x/90+x=19.9

1772+22x=1791+19.9x

2.1x=19

X= 9

Hence the missing frequency 20-24= 9

2. You are supplied the following data about heights of students in a college. Boys Girls

Number 72 38

Average height (inches) 68 61

Variance of distribution 9 4

Find out:

(a). In which sex, boys or girls, is there greater variability in individual heights. (b). Common average heights in boys and girls.

(c). Standard deviation of height of boys and girls taken together. (d). Combined variability.

a. C.V of boys height = σ¹/x×100=√9/68=4.41%

(a) C.V of girls height = σ²/x ×100=√4/61×100=3.28%

Thus there is greater variability in the height of boys than girls,

(b) height of boys and girls combined is

̅x¹²=N¹̅x¹+N²̅x²/N¹+N²=

72×68+38×61/72+38=7214/110=65.58 inches approx.

(c) the combined standard deviation may be calculated by applying the following formula:

72×9+38×4/72+38 + 72(65.58-68)²+38(65.58-61)²/72+38=

2018.794/110=18.35

σ¹²=4.28 inches

(d)combined variability=σ/̅x×100=4.28/65.58×100=6.53.

3. The sales of a company in thousands of Rs for the year 1965 through 1971 are given below:

Estimate the sales figure for the year 1972 using an equation of the form. Y=ab x

where x= year and Y= sales.

Solution :

Below

Taking logs :log Y=loga+xlogb

year

x

y

Log y

x²

x.log y

1965

-3

32

1.5051

9

-4.5153

1966

-2

47

1.6721

4

-3.3442

1967

-1

65

1.8129

1

-1.8129

1968

0

92

1.8318

0

-9.6724

1969

1

132

2.1206

1

+2.1206

1970

2

190

2.2788

4

+4.5576

1971

3

275

2.4393

9

+7.3179

13.9961

13.6606

28

4.3237

Substituting the values in the

Expression

Log a = ∑log Y/N

Log a =13.6606/7=1.9515

Log b =∑log Y/x²

Log b = 4.3237/28 = 0.154

Thus the equation becomes

Log Y = 1.9515+154x .

Origin 1969 time unit =1 year .

For 1972 x would be +4. Putting this value

Log Y = 1.9515+.154(4)

Log Y=1.9515+.6160=2.5675

Log Y=anti log. 2.5675=36.94

Hence the estimated sales for the year 1972 is 385.9 thousand rupees.

Assignment-B

Q1) A die is tossed 120 times with the following results:

No. turned

up

1 2 3 4 5 6 Total

Frequency 30 25 18 10 22 15 120

Test the hypothesis that the die is unbiased.

On the basis of the hypothesis that the die is unbiased.

We should expect each no to turn up 120/6=20 times.

) Ballast must weigh 150 kg. It can be made from two raw materials, A (with a cost of Rs. 20 per unit) and B (with a cost of Rs. 80 per unit). At least 14 units of B and no more than 20 units of A must be used. Each unit of A weighs 5 kg and each unit of B weighs 10 kg. How many units of each type of raw material must be used for a product to minimize cost?

Solution : Interpret the problem:

B >= 14

A c. 0.725 & 0.275

d. 0.650 & 0.650

e. 0.542 & 0.335

2. If you want to test the whether the...

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