Quantitative Techniques In Management

Topics: Sampling, Sample, Stratified sampling Pages: 15 (2670 words) Published: April 21, 2015

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

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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