# N個の和をとるのは製品全体での平均化に相当します

## English translation: Taking the sum of N values is equivalent to taking the average of all the products.

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 08:12 Mar 29, 2007
Japanese to English translations [PRO]
Tech/Engineering - Mathematics & Statistics / quality engineering
 Japanese term or phrase: N個の和をとるのは製品全体での平均化に相当します 積分は製品の寿命における平均化，N個の和をとるのは製品全体での平均化に相当します。 This is describing a loss function.
 caseyUnited States Local time: 15:45
 Explanation:Don't think I am knowledeable enough, but let me give it a try. I assume this is a product test that measures deviations from the target value in N number of different conditions. By summing N number of values and divide it by N, you get the observed average deviation from the target for the product type, which is supposed to give a good estimate of the (population) average deviation for all the products. This Japanese sentence says that the sum corresponds to the average. Although a sum is not an average, it can be used as a substitute, i.e., equivalent, of average if the number of values (N) is constant. The last formula of this page might clarify what this sentence means. In this formula, however, the sum is divided by the number of values (deviations from the target value) to give the average. http://www.mv.com/ipusers/rm/loss.htm
Selected response from:

sigmalanguage
Japan
Local time: 05:45
 Thanks, everyone. I really appreciate the help. 4 KudoZ points were awarded for this answer

3sum of N denotes the leveling of the whole product
 xxxAkiHofmann
3taking the sum over the N products is equivalent to computing the average for all units
 sudo
3Taking the sum of N values is equivalent to taking the average of all the products.
 sigmalanguage

7 hrs   confidence:
Taking the sum of N values is equivalent to taking the average of all the products.

Explanation:
Don't think I am knowledeable enough, but let me give it a try.

I assume this is a product test that measures deviations from the target value in N number of different conditions. By summing N number of values and divide it by N, you get the observed average deviation from the target for the product type, which is supposed to give a good estimate of the (population) average deviation for all the products.

This Japanese sentence says that the sum corresponds to the average. Although a sum is not an average, it can be used as a substitute, i.e., equivalent, of average if the number of values (N) is constant.

The last formula of this page might clarify what this sentence means. In this formula, however, the sum is divided by the number of values (deviations from the target value) to give the average.
http://www.mv.com/ipusers/rm/loss.htm

 sigmalanguageJapanLocal time: 05:45Works in fieldNative speaker of: JapanesePRO pts in category: 8
 Thanks, everyone. I really appreciate the help.

8 hrs   confidence:
taking the sum over the N products is equivalent to computing the average for all units

Explanation:
The precise meaning really depends on the specific form of the loss function and how variables used in the function are defined. But, if I'm allowed to take a wild guess, I would interpret the phrase as follows.

"Taking an integral is equivalent to computing the average (of some value, not specified in the phrase you gave) for the units with a certain life span, whereas taking the sum over the N products is equivalent to computing the average for all units."

There are two averages mentioned. If my guess is right, the former refers to the average for the units that last, say, 10 years, and the latter to the average for all units, regardless of their life span.

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Note added at 8 hrs (2007-03-29 17:03:54 GMT)
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Oops... The title section should have been: "taking the sum over the N UNITS ..."

 sudoUnited StatesLocal time: 15:45Specializes in fieldNative speaker of: JapanesePRO pts in category: 4

11 hrs   confidence:
sum of N denotes the leveling of the whole product

Explanation:
Just another option for you.

Integral denotes leveling due to the product's life span, and sum of N denotes the leveling of the whole product.

 xxxAkiHofmannUnited StatesLocal time: 15:45Native speaker of: Japanese

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