More context for formula wanted

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In summary, the conversation discusses a formula involving a double sum over a set of values v_1, ... , v_n, which is \frac{1}{N^2} \sum_{i<j} (v_i-v_j)^2. The speaker initially thought it was related to variance, but realized it was not the case. They mention that the v_i values are vectors and ask if the formula has a specific name or a simplified version. They suggest it may be a special case of a Mahalanobis distance.
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birulami
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For a set of values [itex]v_1,\dots,v_n[/itex] I recently stumbled over the formula

[tex]\frac{1}{N^2} \sum_{i<j} (v_i-v_j)^2[/tex]

where the sum is meant to be a double sum over j between 1 and N and i between 1 and j. First I thougth it should have something to do with variance. But this is obviously not the case. In my case, the [itex]v_i[/itex] are vectors, but this may or may not be important for the question:

Does this formula ring any bells? Is it something with a name? Does it have an interesting simplification?

Any hints appreciated.
 
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1. What is the purpose of providing more context for a formula?

The purpose of providing more context for a formula is to give a better understanding of the formula and its use. This can help to clarify any confusion or misunderstandings and make it easier to apply the formula in different situations.

2. How can more context be added to a formula?

More context can be added to a formula by including explanatory notes, providing examples, or giving a detailed explanation of the variables and their meanings. Visual aids such as graphs or diagrams can also be used to enhance the understanding of the formula.

3. Why is it important to have a clear understanding of the context for a formula?

Having a clear understanding of the context for a formula is important because it can affect how the formula is used and interpreted. Without proper context, the formula may be applied incorrectly, leading to incorrect results.

4. What are some examples of when providing more context for a formula would be beneficial?

Providing more context for a formula would be beneficial in situations where the formula is complex, has multiple variables, or is used in different scenarios. It can also be helpful when the formula is being used for decision making or analysis.

5. How can adding more context to a formula improve its usefulness?

Adding more context to a formula can improve its usefulness by making it more versatile and applicable to a wider range of situations. It can also make the formula easier to understand and use, leading to more accurate and reliable results.

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