Using gauss backward difference formula estimate the no. of person. Wages(Ro.) belwo40 40-60 60-80 80-100 100-120 No. of person 250 120 100 70 50

Using gauss backward difference formula estimate the no. of person.

Wages(Ro.)    belwo40  40-60 60-80  80-100   100-120

No. of person  250         120    100      70             50

Sol:

u       x        f(x)        ∆f(x)       ∆²f(x)       ∆³f(x)    ∆⁴f(x)

-2    40      250

                                -130

-1   60       120                         110

                                  -20                          -120

0     80      100                          -10                          140

                                 -30                               20

1   100        70                           10

                                 -20

2   120        50

x = a + uh

70  = 80 + u (20)

u = 70 – 80

           20

[ u = -0.5]

f(u) = 100 + (-5)(-30) + (-0.5)(-0.5 – 1)   (-10)

                                                  2

         + (-0.5)(-0.5 – 1)(-0.5 + 1) (20)

                         6

      + (-0.5)(-0.5 – 1)(-0.5 + 1)(-0.5 – 2)  (140)

                         24

= 100 + 15 + (-3.75) + 1.25 + (-5.46875)

=  107.03