Assignment No: 2 (Lessons 10-15)

Question 1:                                                                                                                           Marks: 7

For the given cumulative frequency table of students of different age groups, calculate the coefficient of standard deviation and coefficient of variation.

Age in years

Cumulative frequency of students (cf)

5-8

3

9-12

15

13-16

24

17-20

51

21-24

57

25-28

60

Solution:

 

Age in Years C.F X F Fx Fx2
 5 – 8 3 6.5 3 19.5 126.5
9 – 12 15 10.5 12 126 1323
13 – 16 24 14.5 9 130.5 1892.25
17 – 20 51 18.5 27 499.5 9240.75
21 – 24 57 22.5 6 135 3037.5
25 – 28 60 26.5 3 79.5 2106.75
Total 210 99 60 990 17726.75


Variance =S2 = ∑fx2 / ∑f – (∑fx/∑f)2

17726.75 / 60 – (990/60)2

295.44583 – (16.5)2

295.44583 – 272.25

23.19583

Standard Deviation = √S2 = √23.19583 = 4.816204938

 

Coefficient of Standard Deviation = S/Mean

_

Mean= X = 990/60 = 16.5

S = 4.81620

So                                            4.816204938 / 16.5 = 0.291891208

Coefficient of Variation = 4.81620 / 16.5

= 0.291891208 * 100

Coefficient of Variation = 29.1891208

 

Question 2:                                                                                                                           Marks: 8

From the following data of hours worked in a factory (x) and output units (y), determine the regression line of y on x, the linear correlation coefficient and interpret the result of correlation coefficient.

Hours (X)

91

102

83

93

89

72

82

85

79

Production (Y)

300

302

315

330

300

250

300

340

315

Solution:

X Y X.Y X2 Y2
91 300 27300 8281 90000
102 302 30804 10404 91204
83 315 26145 6889 99225
93 330 30690 8649 108900
89 300 26700 7921 90000
72 250 18000 5184 62500
82 300 24600 6724 90000
85 340 28900 7225 115600
79 315 24885 6241 99225
776 2752 238024 67518 846654

 

∑X =     776

∑Y =     2752

∑X.Y = 238024

∑X2   = 67518

∑Y2   = 846654

 

Regression line Y on X

Byx  =   n∑xy – (∑x) (∑y) / n∑ x2 – (∑x)2

= 9(238024) – (776)(2752) / 9 (67518) – (776)2

= 9(238024) – (2135552) / 9 (67518) – (602176)

= 2142216 – 2135552 / 607662 – 602176

= 6664 / 5486

= 1.2147284

_      _

A  = y –  bx

= ∑y / n – b (∑x/n)

= 2752 /9 – 1.2147284 (776/9)

= 305.77777 – 1.2147284 (86.22222)

= 201.0411907

_

Y= a+bx

= 201.0411904 + 1.2147284

 

Linear Coefficient of Correlation:

 

∑xy – (∑x)(∑y)/n

r = ——————————————–

√ [∑x2 – (∑x)2 / n ] [∑y2 – (∑y)2 / n]

 

(238024) – (776)(2752) /9

=  —————————————————–

√ [67518 – (776)2 / 9] [846654 – (2752)2 / 9]

 

238024 – 237283.5556

= ——————————————————-

√ (67518 – 66908.4444) (846654 – 841500.4444)

740.4444

= ————————–

√ (609.5556) (5153.556)

740.4444

= ——————-

√3141378.92

740.444

= ——————

1772.393557

= 0.417765003

 

  • Alina

    Thanksssssss

  • Irfanarshadfani

    many many thanks dear,
    rana fani
    MBA-II
    MC-110404331

  • Dream Gudya

     thnk u soo much..

  • Minhaj_19999

    thanks yar

    excelllent

    minhaj ud din
    bc0704010981

  • Ghazalkangan

    wrong solution
     

   
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