# 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