Question

If different values of variable x are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5 and 11.1;
find
(i) the mean ` barx `

(ii) the value of  ` sum (x_i - barx)`

Answer 1

(i) The given numbers are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5, 11.1

`barx` = `(x1 + x2 + x3+ x4 + x5+ .......+ xn)/ (n)`

= `( 9.8 + 5.4 + 3.7 + 1.7 + 1.8 + 2.6 + 2.8 + 8.6 + 10.5 + 11.1)/ (10 )`

= 5.8

(ii) The value of `sum_( i =1) ^ 10 ( x_i-barx)`

We know that

`sum_( i = 1)^n( x_i - barx) = (x1-barx) + (x2-barx).........+ (xn-barx) = 0`

Here

` barx ` = 5.8

Therefore

`sum_(i=1)^10 (x_i-barx)`

= ( 9.8 - 5.8) + ( 5.4 - 5.8 ) + (3.7 - 5.8 ) + ( 1.7 - 5.8 ) + ( 1.8 - 5.8 ) + (2.6 - 5.8 ) + (2.8 - 5.8 ) + ( 8.6 - 5.8 ) + ( 10.5 - 5.8 ) + ( 11.1 - 5.8 )

= 4 - 0.4 - 2.1 - 4.1 - 4 - 3.2 - 3 + 2.8 + 4.7 + 5.3

=0