数学好的进一下

lichunyi · 发表于 2008-12-24 11:49:00

以下是引用mypiao在2008-12-24 11:17:00的发言：

没失望,我开始仰视了呵呵

我说我给你信箱发信你怎么不理我啊，原来一直在往上看呢。

活动一下颈椎吧，往下看看我的信。

ciscogeek · 发表于 2008-12-24 22:54:00

也是只知道自由度的说法，N个数，还有平均值，第N个数实际没有信息，已经在均值中体现了。所以只能算N-1

水模样 · 发表于 2008-12-25 10:37:00

Applying this to the original formula for standard deviation gives:
$\begin{align} \sigma & = {} \sqrt{\frac{1}{N} \left(\left(\sum_{i=1}^N x_i^2\right) - N\overline{x}^2\right)} \& {} = \sqrt{\frac{1}{N} \left(\sum_{i=1}^N x_i^2\right) - \overline{x}^2}. \end{align}$

In the real world, finding the standard deviation of an entire population is unrealistic except in certain cases,such as... where every member of a population is sampled. In most cases, the standard deviation is estimated by examining a random sample taken from the population. Using the definition given above for a data set and applying it to a small or moderately-sized sample results in an estimate that tends to be too low. The most common measure used is an adjusted version, the sample standard deviation, which is defined by

$ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}\,, $

where $\scriptstyle\{x_1,\,x_2,\,\ldots,\,x_N\}$ is the sample and $\scriptstyle\overline{x}$ is the mean of the sample. The denominator N − 1 is the number of degrees of freedom in the vector $\scriptstyle(x_1-\overline{x},\,\dots,\,x_N-\overline{x})$ .

水模样 · 发表于 2008-12-25 10:38:00

汗，这个好像跟数学好没啥关系

mypiao · 发表于 2008-12-25 19:05:00

以下是引用水模样在2008-12-25 10:37:00的发言：

Applying this to the original formula for standard deviation gives:
$\begin{align} \sigma & = {} \sqrt{\frac{1}{N} \left(\left(\sum_{i=1}^N x_i^2\right) - N\overline{x}^2\right)} \& {} = \sqrt{\frac{1}{N} \left(\sum_{i=1}^N x_i^2\right) - \overline{x}^2}. \end{align}$

In the real world, finding the standard deviation of an entire population is unrealistic except in certain cases,such as... where every member of a population is sampled. In most cases, the standard deviation is estimated by examining a random sample taken from the population. Using the definition given above for a data set and applying it to a small or moderately-sized sample results in an estimate that tends to be too low. The most common measure used is an adjusted version, the sample standard deviation, which is defined by

$ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}\,, $

where $\scriptstyle\{x_1,\,x_2,\,\ldots,\,x_N\}$ is the sample and $\scriptstyle\overline{x}$ is the mean of the sample. The denominator N − 1 is the number of degrees of freedom in the vector $\scriptstyle(x_1-\overline{x},\,\dots,\,x_N-\overline{x})$ .

多谢啊,这下子真的弄懂了那.

BTW:这个问题还是跟数学有关的吧?在证明向量 $\scriptstyle(x_1-\overline{x},\,\dots,\,x_N-\overline{x})$ 的秩是N-1的时候,还是需要通过数学公式推导的吗

数学好的进一下

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