Question

In an experiment with $15$ observations on $x$, the following results were available $\sum x^2=2830,\sum x=170$ One observation that was $20$, was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is

• A. 9.3
• B. 8.3
• C. 188.6
• D. 177.3
• E. 78

Answer 1

Answer: (E)

We have
$N=15$
Incorrect $\Sigma x_1^{2}i=2830$,
Incorrect $\Sigma x_i=170$
$\therefore$ Correct $\Sigma x_i=$ Incorrect $\Sigma x_i-20+30$
$=170+10$
$=180$
$\therefore$ Correct mean $=\bar{X}=\frac{\Sigma X_i}{N}($ correct $)$
$=\frac{180}{15}$
$=12$
Also, correct $\Sigma x_i^2=$ Incorrect $\Sigma x_i^2-(20{)}^2+(30{)}^2$
$=2830-400+900$
$=2830+500$
$=3330$
$\therefore$ Correct variance $=\frac{\Sigma x_i^2(\text{ correct })}{N}-(\bar{X}{)}^2$
$=\frac{3330}{15}-(12{)}^2$
$=222-144$
$=78$