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In the ordered line : X: 4, 5, 9, 10, 11, 13, 16 P(X) 0.12, 0.1, 0.11,0.11,0.14,0.34,0,08 what is standard deviation? the mean is 10.31 Can you guys help me to find the standard deviation?

Hoàng Oanh Lê
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  • I wanted to you the table to denote: – Hoàng Oanh Lê Apr 02 '20 at 06:14
  • X 4 5 9 10 11 13 16 P(X) 0.12 0.1 0.11 0.11 0.14 0.34 0.08 – Hoàng Oanh Lê Apr 02 '20 at 06:17
  • You have asked : "what is the standard deviation" ; I have answered you in mathematical terms. The way to arrange it into a table is another thing : I would advise you to take a look at your lecture notes for this. What is your level of study ? 5-7 grade in high school ? – Jean Marie Apr 02 '20 at 06:18
  • I knew the formula to find out the standard deviation but I need the answer of standard deviation, not a formula, we all knew how to find the standard deviation. But in this situation, I cannot use the normal formula to solve. Ok, for example, the probability of 4 is 0.12; the probability of 5 is 0.10,... but we do not know how many numbers are there? when I try in a hard way by using my calculator I guess n = 100. well, haha, I must put 100 number into my caculator? That's a stupid way. So, that I mean – Hoàng Oanh Lê Apr 02 '20 at 07:04
  • I beg your pardon, but your question wasn't clear enough. Make a first line with the $X_k$s. Make a second line with the frequencies $p_k$. Make a third line with the squares $(X_k)^2$. Make a fourth line with the $p_k(X_k)^2$. Summing this fourth line and dividing it by $n-1$ will give you $E(X^2)$. Now it remains to subtract $E(X)^2=m^2$ to obtain the variance, then take its square root. – Jean Marie Apr 02 '20 at 07:28
  • never mind. ok, everything is ok. I understood the way to get the answer yesterday. Thank you for your help. I appreciate that. You are smart! totally, Variance = sigma p(x) * [ rx - E(rx)] ^2 and then, take it square root, we have standard deviation. – Hoàng Oanh Lê Apr 03 '20 at 00:40
  • This is not the most efficient formula : consider the alternative formula which under its theoretical form is $V(X)=E(X^2)-E(X)^2$. – Jean Marie Apr 03 '20 at 04:49

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