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
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