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We have used formula formula to calculate weight as,

$$ w_1 = \frac{s_1}{s_1 + s_2 + s_3};$$ $$ w_2 = \frac{s_2}{s_1 + s_2 + s_3};$$ $$ w_3 = \frac{s_3}{s_1 + s_2 + s_3};$$

However, their is possibility of negative and positive numbers. Even all can be negative or positive. How to calculate weight in this type of situation.

For us -/+ are according to strict algebraic rules. i.e bigger the negative number smaller will be its value.

Thanks.

Mahdi Khosravi
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Pranit Kothari
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2 Answers2

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Let the smallest of the numbers $s_1$, $s_2$, $s_3$ be $m$. Let $t_i=s_i-m+1$ for each $i$. Then the $t_i$ are all positive, and satisfy the same order relatins as the $s_i$, for example, if $s_1\lt s_2$, then $t_1\lt t_2$. So you can use your formula to assign weights to the $t_i$, and then assign those same weights to the $s_i$.

Whether you will like the weights you get, I can't say. Experiment a bit and you may find some other constraint you want your weights to satisfy, then we can refine the technique.

Gerry Myerson
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I'm a little confused by your question. When you say the weight can be positive or negative, do you mean just the value can be negative or positive because of the measurement technique, or is it actually a negative weight? I would assume the first (for example, if you slow down really fast in an elevator, and measure your weight in that frame, you'll actually have 'negative' weight).

With that said, I think what you're after is the RMS value (root mean squared). It's a common technique used to measure velocity since velocity is a vector and can have negative components, but often we care only about it's magnitude. If that is the case for your weight, then do the following.

$w1 = (s1^2/(s1^2 + s2^2 + s3^2))^{1/2}$

$w2 = (s2^2/(s1^2 + s2^2 + s3^2))^{1/2}$

$w3 = (s2^2/(s1^2 + s2^2 + s3^2))^{1/2}$

If you indeed just want the average and weight can be negative, do exactly as what the formulas you provided for us tell you to do.

Spaderdabomb
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  • Weight will not be positive/neg, only numbers – Pranit Kothari Jul 26 '13 at 07:40
  • Does RMS is not making all the values to positive by squaring them.. how in this formula, +ve nad -ve treated differently? – Pranit Kothari Jul 26 '13 at 07:46
  • What's the problem then? Just calculate the average from the formulas you gave me? I don't see the difference between this problem and a normal averaging problem, maybe give more context of the problem? It's unclear what you mean by "However, their is possibility of negative and positive numbers. Even all can be negative or positive. How to calculate weight in this type of situation." – Spaderdabomb Jul 26 '13 at 07:46
  • The point of rms is to get rid of the negative sign so we know the MAGNITUDE. If you want to keep the negative sign, just average normally – Spaderdabomb Jul 26 '13 at 07:47
  • if numbers are say -1 -2 -3, then with my formula -3 will have biggest weight. But practically it should have smallest weight because it is negative number. – Pranit Kothari Jul 26 '13 at 07:49
  • Why will it have the biggest weight? Your answer should follow the same rules as what you're defining in the beginning of the problem no? So if you have an average of -1, -2, and -3, your average is -2. Now if you average -1, -1, -1, you get -1. Clearly in the second example, the weights should be 'bigger' since they are smaller negative numbers. Your answer also should follow the same rules. Therefore, your average of -2 should represent a smaller weight then an answer of -1. I don't see the problem? – Spaderdabomb Jul 26 '13 at 08:04