0
$\begingroup$

$$N=30 \\ \sum_{i=1}^{30}x_i=120 \\ \\ \sum_{i=1}^{30}x_i^{2}=750\\ $$

Find a standard deviation of x:

$$ \bar{x}=\frac{120}{30}=4 \\ sd=\sqrt[]{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^{2}}{N}}=\sqrt[]{\frac{\sum_{i=1}^{n}(x_i^{2}-2\bar{x}x_i+\bar{x}^{2})}{N}}=\sqrt[]{\frac{\sum_{i=1}^{n}x_i^{2}-2n\bar{x}\sum_{i=1}^{n}x_i+n\bar{x}^{2}}{N}}=\sqrt[]{\frac{750-2*30*4*120+30*{4}^{2}}{30}}=30.1$$

But in the textbook the answer is 4

$\endgroup$
1
$\begingroup$

There is another formula for the variance of a random variable derived from the first and second moments.

$Var(X)=E((X-\mu)^2)=E(X^2)-E(\mu)^2=E(X^2)-\mu^2$.

As it turns out, you have all the information you need to estimate this.

$\endgroup$
6
  • $\begingroup$ Oh my god, I forgot about that formula. Thanks. But it gives a different answer (27) $\endgroup$ – PHP Useless Jan 19 at 11:50
  • $\begingroup$ @PHPUseless Are you sure about that? Is that the result of the variance of $X$ or the standard deviation of $X$? $\endgroup$ – user2974951 Jan 19 at 11:59
  • $\begingroup$ yeah, sd=sqrt(27), it is about 5, but the answer is 4. And what's wrong with my calculation? $\endgroup$ – PHP Useless Jan 19 at 12:13
  • $\begingroup$ @PHPUseless $SD(X)=\sqrt{750/30-(120/30)^2}=3$ for me. $\endgroup$ – user2974951 Jan 20 at 9:50
  • $\begingroup$ why should we divide 750 by N=30? $\endgroup$ – PHP Useless Jan 24 at 18:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.