Question

if x bar is the arithmetic mean of n observations x1,x2,x3,.....,xn,then prove that value of (x1-xbar)+(x2-xbar）+(xn-xbar）= 0 MATH QUESTION IF X BAR IS THE EARTH MATIC MEAN OF AN OBSERVATION X1 X2 X3 DASH DASH DASH ACTION THEN PROVE THAT X 1 - X SQUARE + X 2 - X SQUARE + X 3 - XY + 10 DAYS IF X MINUS X BAR IS EQUAL TO ZERO

Answer 1

a/c to question,

arithmetic mean of $x_1,x_2,x_3$.... $x_n$ is $\bar{x}$

so, $\bar{x}=\frac{x_1+x_2+x_3+....+x_n}{n}$

$\implies x_1+x_2+x_3+....+x_n=n\bar{x}$......(1)

now, $LHS=(x_1-\bar{x})+(x_2-\bar{x})+(x_3-\bar{x})+.......+(x_n-\bar{x})$

= $(x_1+x_2+x_3+.....+x_n)-(\bar{x}+\bar{x}+\bar{x}+.....+\bar{x})$

= $(x_1+x_2+x_3+....+x_n)-n\bar{x}$

from equation (1),

= $n\bar{x}-n\bar{x}=0=RHS$

Answer 2

Answer:

/c to question,

arithmetic mean of x_1,x_2,x_3x

1

,x

2

,x

3

.... x_nx

n

is \bar{x}

x

ˉ

so, \bar{x}=\frac{x_1+x_2+x_3+....+x_n}{n}

x

ˉ

=

n

x

1

+x

2

+x

3

+....+x

n

\implies x_1+x_2+x_3+....+x_n=n\bar{x}⟹x

1

+x

2

+x

3

+....+x

n

=n

x

ˉ

......(1)

now, LHS=(x_1-\bar{x})+(x_2-\bar{x})+(x_3-\bar{x})+.......+(x_n-\bar{x})LHS=(x

1

−

x

ˉ

)+(x

2

−

x

ˉ

)+(x

3

−

x

ˉ

)+.......+(x

n

−

x

ˉ

)

= (x_1+x_2+x_3+.....+x_n)-(\bar{x}+\bar{x}+\bar{x}+.....+\bar{x})(x

1

+x

2

+x

3

+.....+x

n

)−(

x

ˉ

+

x

ˉ

+

x

ˉ

+.....+

x

ˉ

)

= (x_1+x_2+x_3+....+x_n)-n\bar{x}(x

1

+x

2

+x

3

+....+x

n

)−n

x

ˉ

from equation (1),

= n\bar{x}-n\bar{x}=0=RHSn

x

ˉ

−n

x

ˉ

=0=RHS