南哥 asked in 科學數學 · 8 years ago

工程統計 標準差

Programmer Design Language 1 Design Language 2 Difference

1 17 18 -1

2 16 14 2

3 21 19 2

4 14 11 3

5 18 23 -5

6 24 21 3

7 16 10 6

8 14 13 1

9 21 19 2

10 23 24 -1

11 13 15 -2

12 18 20 -2

sD≒2.96 (好像是標準差) 請問這個數字是如何算出來的 要詳細算法

3 Answers

Rating
  • 8 years ago
    Favorite Answer

    Xi : Difference of Programmer i

    Mean

    = [Σ(i = 1 to 12) xi]/ n

    = [(-1) + 2 + 2 + 3 + (-5) + 3 + 6 + 1 + 2 + (-1) + (-2) + (-2)] / 12

    = 2/3

    Standard deviation (s.d.)

    = √{[2(-1 - 2/3)² + 3(2 - 2/3)² + 2(3 - 2/3)² + (-5- 2/3)² + (6 - 2/3)² + (1 - 2/3)² + 2(-2 - 2/3)²] / 12}

    = √(96.67 / 12)

    ≈ 2.96

    2012-06-24 01:20:17 補充:

    打錯字,standard deviation (s.d.) 的算式中,分子應為 11 而並非 12。

    Source(s): 胡雪, 胡雪
  • 楓葉
    Lv 4
    8 years ago

    將所有數平均之後會得到平均數

    每個數減掉平均數後再平方,最後加起來除以數字有多少個

    就是標準差

  • 麻辣
    Lv 7
    8 years ago

    A=(-1,2,2,3,-5,3,6,1,2,-1,-2,-2)Xbar=(-1+2+2+3-5+3+6+1+2-1-2-2)/12=2/3Let Xb=Xbar, m=n-1=12-1=11(樣本少數改用n-1)Var=Σ(X-Xb)^2/m=(ΣX^2-2XbΣX+ΣXb^2)/m=(ΣX^2-2Xb*nΣX/n+ΣXb^2)/m=(ΣX^2-2Xb^2*n+Xb^2*n)/m=(ΣX^2-Xb^2*n)/m=(102-4*12/9)/11=(102-16/3)/11=(306-16)/33=290/33=8.78787879where ΣX^2=1*3+4*5+9*2+25+36=102S=√Var=√(290/33)=2.964435661

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