Chinese term (edited): ����ֵ 5 �˜ʲ� 1

中心值 5 標準差 1:
central value 5 and standard deviattion 1 or:
central value 5 and root-mean-square deviattion 1.

Chinese term (edited): ����ֵ 5 �˜ʲ� 1

Median
The median is the value halfway through the ordered data set, below and above which there lies an equal number of data values.
http://www.cas.lancs.ac.uk/glossary_v1.1/presdata.html#med

Standard Deviation
Standard deviation is a measure of the spread or dispersion of a set of data.
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It is calculated by taking the square root of the variance and is symbolised by s.d, or s. That is:
　　　　　　　　　＿＿　　 ＿＿
　　　　　　　　√V(X) = √σ^2 = s
The more widely the values are spread out, the larger the standard deviation. For example, say we have two separate lists of exam results from a class of 30 students; one ranges from 31% to 98%, the other from 82% to 93%, then the standard deviation would be larger for the results of the first exam.
http://www.cas.lancs.ac.uk/glossary_v1.1/presdata.html#stand...

Sample Mean
The sample mean is an estimator available for estimating the population mean . It is a measure of location, commonly called the average, often symbolised -x.
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Example
Lets say our data set is: 5 3 54 93 83 22 17 19.
The sample mean is calculated by taking the sum of all the data values and dividing by the total number of data values:

　　　　　　　　　　5+3+54+93+83+22+17+19
　　　　　　-x = ------------------------- = 37
　　　　　　　　　　　　　　　8
Its value depends equally on all of the data which may include outliers. It may not appear representative of the central region for skewed data sets.
It is especially useful as being representative of the whole sample for use in subsequent calculations.
http://www.cas.lancs.ac.uk/glossary_v1.1/presdata.html#sampm...

2. Mean and standard deviation
The median is known as a measure of location; that is, it tells us where the data are. As stated in , we do not need to know all the exact values to calculate the median; if we made the smallest value even smaller or the largest value even larger, it would not change the value of the median. Thus the median does not use all the information in the data and so it can be shown to be less efficient than the mean or average, which does use all values of the data. To calculate the mean we add up the observed values and divide by the number of them.The total of the values obtained in Table 1.1 was 22.5μmol/24hr, which was divided by their number, 15, to give a mean of 1.5μmol/24hr. This familiar process is conveniently expressed by the following symbols:

　　　　　　　　　(Σx)
　　　　　　-x = ------
　　　　　　　　　　n　　
-x(pronounced "x bar") signifies the mean; x is each of the values of urinary lead; n is the number of these values; and , the Greek capital sigma (our "S") denotes "sum of". A major disadvantage of the mean is that it is sensitive to outlying points. For example, replacing 2.2 by 22 in Table 1.1 increases the mean to 2.82μmol/24hr, whereas the median will be unchanged.
http://bmj.bmjjournals.com/collections/statsbk/2.shtml

Judging with the explanations of the above links, I have to say that "median" is meant in your case, not "mean," because (Σ1..9)/9 doesn't equal to 5. The number 5 is obviously the "median," not the "mean."


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Note added at 7 hrs 12 mins (2004-08-07 16:42:01 GMT)
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Ooops, (Σ1..9)/9 = (1+9)/2 =5 !
It is the mean and the median!

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Note added at 7 hrs 13 mins (2004-08-07 16:42:46 GMT)
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I mean in this special case.

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Note added at 7 hrs 38 mins (2004-08-07 17:08:36 GMT)
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The reason why the median equals to the mean is that the SD equals to one.
Should the SD differ from one, the median would differ from the mean.

Chinese term (edited): ����ֵ 5 �˜ʲ� 1

Although the word median does appear to be the correct translation of the word 中心, it is unusual for the median and standard deviation to be mentioned together with no mention of the mean. This is because the standard deviation cannot be calculated without the mean and the mean can be determined independently of both the mean and standard deviation.

I suggest you check with the author, or verify within the text that it is indeed the median that is meant.



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Note added at 2 hrs 50 mins (2004-08-07 12:20:41 GMT)
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The passage \"Although the word median does appear to be the correct translation of the word 中心, it is unusual for the median and standard deviation to be mentioned together with no mention of the mean. This is because the standard deviation cannot be calculated without the mean and the mean can be determined independently of both the mean and standard deviation\" should have read:

\"Although the word median does appear to be the correct translation of the word 中心, it is unusual for the median and standard deviation to be mentioned together with no mention of the mean. This is because the standard deviation cannot be calculated without the mean and the median can be determined independently of both the mean and standard deviation.\"

My apologies to HymnLau, if this created confusion for him.


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Note added at 2 hrs 58 mins (2004-08-07 12:28:15 GMT)
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Finally, a normal distribution is defined by two parameters: the mean and standard deviation. Without knowledge of these there can be no normal distribution. This is further evidence to warrant consultation with the author or a sound understanding of the text.

Please do not translate something that you do not understand, even if it makes grammatical sense.

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Note added at 12 hrs 20 mins (2004-08-07 21:49:59 GMT)
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Wenjer Leuschel: After having read your further note I offer the following comment. You have done exactly what I have suggested the translator do, verify within the text whether the median is truly what the author meant to say. So, why do you write disagree.

Finally, although the values of the mean and median can be the same in special cases, by definition they are very different statistics measuring two very different phenomena.



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Note added at 18 hrs 19 mins (2004-08-08 03:49:37 GMT)
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With regard to Yan Li\'s entry I would avoid the term root-mean-square, as the standard deviation is a special use of the root-mean-square. Whereas the root-mean-square is a geometric measure of central tendency, the standard deviation is an average measure of dispersion.

According to the following link physical scientists sometimes confound the two terms, but such confusion would probably not be well received by statisticians. Certainly, I have never seen these terms confounded in economics.

http://mathworld.wolfram.com/Root-Mean-Square.html

By the way, <mathworld.wolfram.com> appears to be an excellent online source for many questions related to mathematics. It could even help Yan Li with his spelling of mathematical terms!