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 the value of $\Sigma (x-\overline{x})$.

• A. $0$
• B. $1$
• C. $5$
• D. $7$

Answer 1

The correct option is A $0$

The values are: $9.8,5.4,3.7,1.7,1.8,2.6,2.8,8.6,10.5$ and $11.1$.

We know, Mean is given by,

$\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$.

Here, number of observations $=10$.

Then, Mean = $\frac{9.8+5.4+3.7+1.7+1.8+2.6+2.8+8.6+10.5+11.1}{10}$

$⟹$ Mean $\overline{x}=\frac{58}{10}$ = $5.8$.

Now,

$\sum (x-\overline{x})$ $=(9.8-5.8)+(5.4-5.8)+(3.7-5.8)+(1.7-5.8)+(1.8-5.8)$

$+(2.6-5.8)+(2.8-5.8)+(8.6-5.8)+(10.5-5.8)+(11.1-5.8)$
$=4-0.4-2.1-4.1-4-3.2-3.0+2.8+4.7+5.3$
$=16.8-16.8=0$.

Therefore, option $A$ is correct.