Question

Sum of squares of deviation of $10$ observations measured from $5$ is $17$ and sum of squares of observations is $170$ then mean of observation is

• A. $40.3$
• B. $4.5$
• C. $4$
• D. $4.03$

Answer 1

The correct option is D $4.03$

Let the observation be $x_1,x_2,x_3,....,x_{10}$

As per Question

$x_1^2+x_2^2+...+x_{10}^2=170$

Mean M=$\frac{x_1+x_2+....+x_{10}}{10}$

$\therefore x_1+x_2+....+x_{10}=10M-\left(1\right)$

also

$(x_1-5{)}^2+(x_2-5{)}^2+;.....+(x_{10}-5{)}^2=17$

$x_1^2+x_2^2+...+x_{10}^2-10(x_1+x_2+.....+x_{10})+25\times 10=17⟹170-10\left(10M\right)+250=17⟹420-100M=17⟹100M=403⟹M=4.03$