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匿名 發問於 科學及數學數學 · 1 十年前

standard deviation一問

知道一堆data個mean同standard deviation

之後改一個data, mean改變左, 咁點計個新standard deviation?

thank you

2 個解答

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  • 1 十年前
    最愛解答

    mean (平均數) , standard deviation (標準差)

    variance (方差)

    e.g. 1, 3, 5, 7, 9

    mean

    =sum of data / number of data

    = (1+3+5+7+9) / 5

    = 25/ 5

    = 5

    standard deviation

    = square root of variance

    variance

    = (1/N * sum of square of data) - square of mean

    = [1/5 * (1² + 3² + 5² + 7² + 9²)] - 5²

    =[1/5 * (1 + 9 + 25 + 49 + 81)] - 25

    =(1/5 * 165) - 25

    =33 - 25

    =8

    (N menas number of data)

    standard deviation (標準差)

    =square root of variance

    =square root of 8

    =2.8284 (to 4 d. p.)

    “Given 一堆data個 mean 同 standard deviation

    之後 改一個data, mean 改變左, 點計個新standard deviation” ?

    example as follow :

    Given : {1, 3, 5, 7, 9}

    mean is 5

    standard deviation is 2.8284 (to 4 d. p.)

    改一個data (change a data)

    new set of data {1, 3, 6, 7, 9}

    mean

    = sum of data / number of data

    = (1 + 3 + 6 + 7 + 9) / 5

    = 5.2

    variance

    =[ 1/ N * (sum of square of data)] - square of mean

    =[ 1/ 5 * (1² + 3² + 6² + 7² + 9²)] - (5.2)²

    =(1/ 5 * 176) - 27.04

    = 8.16

    standard deviation

    = square root of variance

    = square root of 8.16

    = 2.8566 (to 4 d. p.)

    given a set of data,

    to calculate standard deviation (標準差)

    formula (公式) as follow :

    standard deviation

    = square root (平方根) of variance (方差)

    (which) variance is

    (1/N * sum of square of data) - mean²

    hope it is useful

    2006-11-17 15:58:07 補充:

    “知道一堆data個mean同standard deviation之後改一個data, mean改變左, 咁點計個新standard deviation” ?your question is not clearsuppose we known a group of data's - mean- standard deviation- number之後改一個data, suppose we know the changed data (old one & new one)

    2006-11-17 15:59:15 補充:

    example as follow :Given : a groud of data's - mean is 5- standard deviation is 2.8284 (to 4 d. p.)- number is 5 改一個data (change a data)change it to 6 (the old one is 5)

    2006-11-17 16:01:16 補充:

    (suggestion solution) new mean= sum of data / number of data= (5 * 5 - 5 + 6) / 5= 5.2 variance =[ 1/ N * (sum of square of data)] - square of mean={ 1/ 5 * [(2.82842 + 52)5 - 52 + 62] } - (5.2)2 = 8.16

    2006-11-17 16:05:33 補充:

    standard deviation= square root of variance= square root of 8.16= 2.8566 (to 4 d. p.) (I am a student who is studying Maths. & Sta.It is a great idea if you can provide a completed question 完整的問題 which is 用作 學術交流)

  • 1 十年前

    答得好好呀, 又清楚!

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