樣本標準差作母群體標準差估計值,分母要除以n-1  為什麼呢

樣本標準差作母群體標準差估計值,分母要除以n-1  為什麼呢?

@@"請各位大大幫我解題謝謝

Update:

間隔數?是指?

2 Answers

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  • 1 decade ago
    Favorite Answer

    樣本標準差作母群體標準差估計值,分母要除以n-1,為什麼呢?

    在EXCEL中,樣本變異數的函數是"=var"(也就是除以n-1),母群體變異數的函數是"=varp"(也就是除以n)。

    VAR:Estimates variance based on a sample.

    VARP:Calculates variance based on the entire population.

    同樣地,樣本變異數的函數是"=stdev"(也就是除以n-1),母群體變異數的函數是"=stdevp"(也就是除以n)。

    以{-1000,100,100,1068}五個數字為例,如果是母群體的五個數字,則 "=STDEVP({-1000,100,100,1068})" = 731.89;但如果是來自樣本的五個數字,則 "=STDEV({-1000,100,100,1068})" = 845.12

    STDEV: Estimates standard deviation based on a sample. The standard deviation is a measure of how widely values are dispersed from the average value (the mean).

    STDEVP: Calculates standard deviation based on the entire population given as arguments.

    圖片參考:http://img169.imageshack.us/img169/6084/a1ww8.png

    圖片參考:http://img257.imageshack.us/img257/8971/a2ry9.png

    結論:樣本變異數公式為何比群體變異數的公式分母要除以n-1?原因是,這樣才可以得到樣本變異數的不偏估計式,使樣本變異數這個統計量的期望值等於群體變異數。

  • 1 decade ago

    簡單的說

    因為母體資料是經過普查所得,所以除以n

    而樣本是經過抽查(抽樣調查)而得,所以取其間隔數n-1

    Source(s): 數學傳播29卷1期民94年3月
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